JP5987720B2 - Binary decision graph processing system and method - Google Patents

Description

  The present invention relates to a binary decision graph processing system and method.

  Binary decision diagram (hereinafter referred to simply as BDD) compresses logical functions and combinatorial sets in mathematical engineering problems such as VLSI logic design and power distribution system configuration optimization. It is one of the technologies to express and process.

  BDD can be obtained by expressing the result divided into cases for all variables of a given logical function value as a binary tree graph and compressing (reducing) the result. During compression, the order of the variables to be classified is fixed, redundant nodes are deleted, and equivalent nodes are shared as much as possible to obtain an irreducible BDD. This irreducible BDD can uniquely represent a logical function in a compact manner.

For example, in a power distribution network of a power distribution system, power is sent from a substation to a business office or household. There are many switches for switching the route of this distribution network, and it is necessary to select one of many combinations as the optimum route by turning it on and off. There are constraints to consider when trying to optimize a distribution network. Examples of constraints include geometric constraints such as “Do not power out each household and connect two substations” and electrical constraints such as “Do not exceed the allowable current in each section of the wire”. Exists. The BDD can be used to extract a distribution path that satisfies both the geometric constraint condition and the electrical constraint condition. That is, each switch is a node of the graph, and the on state of the switch corresponds to the state where the node value is “1”, and the off state of the switch corresponds to the state where the node value is “0”. For example, if there are N switches, there are 2 ^N combinations, which correspond to a binary tree graph with 2 ^N ends. It is known that an optimum route can be searched at high speed by using BDD obtained by compressing this graph.

  Attempts to further increase the speed by parallelizing BDD processing are also known. For example, there is known a method in which BDD is divided into upper graphs and divided into subgraphs and processed independently. There is also known a method of performing distributed processing for each level of a binary tree graph, that is, by cutting a horizontal row of the binary tree graph.

Takeshi Inoue et al. “Exhaustive search method for distribution network configuration satisfying system operation constraints using ZDD” 2012 Annual Conference of the Institute of Electrical Engineers of Japan, 6th volume, p. 52 Shinichi Tsuji and Shinya Ishihara “Stream type BDD processing algorithm that operates within a certain range of real memory regardless of the size of BDD” System LSI Design Technology 93-9 (1999. 11.27) p. 63 R. E. Bayant, “Graph-Based Algorithms for Boolean Function Manipulation”, IEEE Trans. on Computers, Vol. C-35, No. 8 p. 677 (1986)

  When BDD is implemented as a computer program, BDD grows as the number of nodes increases. At this time, data relating to the nodes of the BDD is stored in the memory as array data. Since the memory capacity of the computer's memory is finite, there is an upper limit on the number of nodes that can be stored. When the BDD grows and exceeds the upper limit value, it may end abnormally or the processing speed may decrease. By dividing the BDD and allocating subproblems to a plurality of computers and processing each subproblem independently, the possibility of memory shortage exceeding the storage capacity of the computer that processes each subproblem can be reduced. . When BDD processing is parallelized, a large proportion of processing time may be communication time for data exchange between computers. Furthermore, there may be many solutions that satisfy the constraint conditions in each subproblem. Then, it takes a lot of communication time to communicate the solution of each partial problem, and there is a problem that it takes a processing time.

  Therefore, as one aspect, the present invention reduces the possibility of memory shortage and reduces the communication time, for example, when dividing a binary decision graph (BDD) and assigning a partial problem to a plurality of computers. It is an object to provide a binary decision graph processing system and method that reduces processing time.

A binary decision graph processing system is provided that includes a master device and a local device.
The master device transmits a sub-problem dividing unit that divides the whole problem into a plurality of sub-problems and at least two sub-problems of the plurality of sub-problems to the local device, and represents solutions of at least two sub-problems from the local device And a master input / output control unit that receives one binary decision graph (BDD). The local device receives at least two subproblems from the master device and transmits a binary decision graph (BDD) representing solutions of the at least two subproblems, and each of the at least two subproblems When the binary decision graphs representing the solutions of the two are created and the binary decision graphs representing the respective solutions satisfy a predetermined condition, the binary decision graphs representing the respective solutions of at least two subproblems are calculated to calculate 1 A local BDD operation unit that generates two binary decision graphs, and a local constraint satisfaction check unit that determines whether the binary decision graph generated by the local BDD operation unit satisfies a constraint condition.

  When dividing the binary decision graph and assigning a partial problem to a plurality of computers, the processing time can be reduced by reducing the communication time, for example, while reducing the possibility of memory shortage.

It is a figure which shows the example of the calculation which produces | generates a binary decision graph (BDD) from a binary tree graph. It is a figure explaining one characteristic of BDD. It is a figure explaining another characteristic of BDD. It is a figure explaining the example of application of BDD. It is a figure explaining a comparative example. It is a figure explaining another comparative example. It is a figure explaining the outline | summary of the parallel processing according to 1st Embodiment. It is a figure which shows the example of the functional block of a master device. It is a figure which shows the example of the functional block of the local device for performing the parallel processing according to 1st Embodiment. It is a figure explaining communication between a master device and a local device. It is a figure which shows the example of BDD sent by communication between the master device shown by FIG. 8, and a local device. It is a figure which shows the example of a structure of a master device and a local device. It is a figure which shows the example of the flow of a process of the parallel processing method according to 1st Embodiment. It is a figure explaining the parallel processing method according to 2nd Embodiment. It is a figure which shows the example of the functional block of the local device for performing the parallel processing according to 2nd Embodiment. It is a figure which shows the example of the flow of a process of the parallel processing method according to 2nd Embodiment. It is a figure which shows the example of the functional block of the local device for performing the modification of the parallel processing according to 2nd Embodiment. It is a figure which shows the modification of the flow of a process of the parallel processing method according to 2nd Embodiment.

  In the following, when the combinatorial optimization problem is calculated by a plurality of computers (devices including a processor) using a binary decision diagram (hereinafter sometimes simply referred to as BDD), the entire problem is divided into each computer. A system and method for reducing processing time and speeding up BDD operations are provided by allocating the obtained subproblems and communicating BDDs representing solutions of the subproblems assigned in each computer. The overall problem can be reduced to the calculation of logic functions such as output function of logic circuit, enumeration of switch ON / OFF with restrictions on combinations, or selection enumeration of selection / non-selection of items with restrictions on combinations. It can be a problem.

  Further, when the combinatorial optimization problem is calculated by a plurality of computers using BDD, a subproblem is assigned to each computer, and the size sum of the individual BDDs of the subproblems assigned in each computer is multiplied by the product of the BDDs of the subproblems. Comparing the size of the BDD after taking (AND operation), and communicating the smaller one, a processing method and apparatus for reducing the processing time and speeding up the BDD operation are provided. As described above, the communication overhead can be reduced by selecting the computer that performs the calculation so that the BDD to be communicated is reduced or the entire processing time is reduced. As a result, the overall calculation time can be reduced by parallelization.

  The parallel computation device and method of the binary decision graph described below is not limited to the case where the BDD representing the solution of the entire problem is obtained by the product (AND operation) of the BDD representing the solution of the subproblem. Even when the BDD to be expressed is obtained by the sum (OR operation) of BDDs representing the solutions of the subproblems, the present invention can be easily modified and applied.

<First Embodiment>
A binary decision graph processing system and method according to the first embodiment will be described with reference to FIGS.

<< General description >>
A binary decision diagram (hereinafter referred to simply as BDD) is a binary tree graph showing the result of dividing all variables of a given logical function value, and compressing (reducing) the binary decision graph (binary decision diagram). Can be obtained. During compression, the order of the variables to be classified is fixed, redundant nodes are deleted, and equivalent nodes are shared as much as possible to obtain an irreducible BDD. This irreducible BDD can uniquely represent a logical function in a compact manner.

Hereinafter, an arithmetic device and method for processing at high speed by parallelizing BDD operations will be described.
As a logical function, a function f (x ₁ , x ₂ , x ₃ ) having an input / output relationship shown in the truth table as shown in Table ₁ is considered. Table 1 shows the result of dividing the value of the logical function f for all variables. In the following, binary logic is considered and true is represented by “1” and false is represented by “0”, but is not limited to {true, false} = {1, 0}. For example, {true, false} = {1 , −1} or other values.

Table 1 shows that, for example, if x ₁ = 0, x ₂ = 0, and x ₃ = 0, f (x ₁ , x ₂ , x ₃ ) = 0.

FIG. 1 is a diagram illustrating an example of a calculation for generating a binary decision graph (BDD) from a binary tree graph.
FIG. 1A is a binary tree graph showing the result of dividing the values of the logical function f shown in the truth table of Table 1 for all variables. In order to obtain the BDD 12 of FIG. 1C from the binary tree graph 10 of FIG. 1A through the quasi-irreducible BDD 11 of FIG. 1B, the order of variables divided into cases is fixed, and equivalent nodes are shared. And delete redundant nodes as much as possible. The operations of sharing equivalent nodes and deleting redundant nodes may be referred to as reduction or compression.

A quasi-irreducible BDD 11 in FIG. 1B is an example of a quasi-irreducible BDD obtained by performing a reduction operation that shares an equivalent node in the binary tree graph 10 in FIG. Node 101 and node 102 in FIG. 1A are equivalent. Here, the “nodes are equivalent” are nodes in which the nodes pointed to by the 0 branch are the same leaf or equivalent, and the nodes pointed to by the 1 branch are the same leaf or equivalent. The binary tree graph 10 in FIG. 1 (a), outputs "1" when "x _3" is "0", the node 101 "x _3" is for outputting "0" when "1" , 102 exist. These two nodes 101 and 102 are equivalent nodes.

The BDD 12 in FIG. 1C is a BDD obtained by performing a reduction operation for deleting redundant nodes in the semi-irreducible BDD 11 in FIG. A “redundant node” is a node whose output value is the same regardless of the value of the variable assigned to the node with respect to the input. For example, in the node 113 of the quasi-irreducible BDD 11 in FIG. 1B, whether the value “x ₃ ” assigned to the node 113 is “1” or “0” is “0” shown in the leaf 115. Is output. Further, in the node 114 of the quasi-irreducible BDD 11 in FIG. 1B, the value “x ₃ ” given to the node 113 is “1” indicated by the leaf 116 regardless of whether it is “1” or “0”. Is output. Thus, the nodes 113 and 114 are redundant nodes.

2A and 2B are diagrams for explaining the characteristics of BDD.
As a feature of BDD, as shown in FIG. 2A, logical operation processing between BDD 131 and BDD 132 can be performed. In FIG. 2A, BDD 133 is obtained by performing an OR operation with BDD 131 and BDD 132.

A basic algorithm of logical operation between BDDs may include the following processing.
(A1) In the binomial operation (f · g), two BDDs are classified for a certain input variable x, and two partial operations (f _{(x = 0)} · g _{(x = 0)} ) and (f _{(x = 1)} · g _{(x = 1)} )
(A2) The decomposition of (A1) is recursively repeated for all input variables, and a BDD as a result of the partial operation is generated when the operation is finally obvious.
(A3) The BDD obtained by each partial calculation is reassembled to generate a BDD representing the entire calculation result.

  Further, it is known that a logical operation can be performed in a time substantially proportional to the number of BDD nodes by using a technique that avoids redundant partial operations.

  Further, as shown in FIG. 2B, for example, an optimum path can be searched by assigning a weight to each node of the reduced BDD. In FIG. 2B, it is possible to search for a path that minimizes the sum of weights from the vertex of the BDD 141 to the leaf representing “1”.

  FIG. 3 is a diagram for explaining a search for a distribution network configuration as an example of searching for an optimal combination using BDD. The problem of configuring the distribution network is sometimes referred to as a distribution network configuration problem. The overall problem is expressed as a calculation of a logical function, including derivation of the output function of the logic circuit, enumeration of on / off combinations of switches that are constrained in combination, and enumeration of selection or non-selection of items that are constrained in combination May be a problem. In the example shown in FIG. 3, the overall problem is a problem of finding a combination of switch states that satisfy the constraint conditions in a system including a power source, a large number of switches, electric wires connecting the switches, and a load connected to the electric wires. The distribution network configuration problem is defined as: (C1) Geometric constraint condition, (C2) Electrical constraint condition, and (C3) Optimal configuration condition as follows.

  Generally, power systems include a power transmission network and a power distribution network. In the power transmission network, electric power is transmitted over a long distance at a high voltage. In the power distribution network, power is sent to each house in a short distance area at a relatively low voltage (several thousand volts). There are many switches in the distribution network, and the distribution network is configured by a combination of the states of the switches (ON (ON) or OFF (OFF)). The distribution network is configured such that a plurality of substations supply power to a predetermined area. If not configured correctly, problems such as power outages, abnormal voltages, and overcurrents may occur.

As shown in FIG. 3, in the distribution network 15, in order to distribute the power from the substations 1501, 1502, 1503, and 1504 to each home, the states of the switches 1511, 1512, 1513, and 1514 are as follows. Must be determined under constraints.
(C1) Geometric constraints (C2) Electrical constraints (C3) Optimal configuration conditions

The geometrical constraint condition (C1) is as follows in the distribution network configuration problem.
(C1-1) An area composed of houses connected to each other when the switch is on is always connected to one substation.
The condition of (C1-1) can be paraphrased as not having a power failure and not connecting different substation systems to one house. There are many such combinations in the power distribution network 15 shown in FIG.

The electrical constraint condition (C-2) is as follows in the distribution network configuration problem.
(C2-1) The current flowing in each section of the electric wire does not exceed the allowable current.
(C2-2) The voltage effect due to the resistance of the electric wire does not exceed the allowable range.
(C2-3) The three-phase alternating current must be balanced.
Etc. In order to determine whether or not the condition (C-2) is satisfied, it is necessary to calculate a current flowing through the electric wire for a given distribution network configuration. They are performed by the distribution network simulator 16 of FIG.

The condition of the optimal configuration of (C-3) can be, for example, a condition of minimum power transmission loss.
In an actual distribution network configuration problem, the number of possible configurations may exceed 2 = ^N and N = 400.

  In a distribution network configuration problem, the entire distribution network may be divided into components that can partially calculate losses. For example, in the minimum loss configuration, assume that the switch near the substation is not open, and assume that the switch from the substation to the first branch point is bound. Then, by dividing the distribution network at the branch point, A component with no spills is obtained and the loss can be calculated independently of the other components. In the following, this situation is mainly considered.

  The BDD computing device 17 creates a BDD 171 from the distribution network 15 and selects a distribution network that satisfies the geometric constraint condition (C1) and the electrical constraint condition (C2). When creating a BDD from the distribution network 15, the node of the BDD corresponds to a switch. Whether the combination of the switch states satisfies the geometric constraint (C1) and the electrical constraint (C2) corresponds to the leaf state “1” or “0”.

  The BDD computing device 17 further satisfies a condition (C-3) among combinations of switches satisfying the geometric constraint condition (C1) and the electrical constraint condition (C2), for example, the transmission loss is minimized. Find the right composition. That is, the BDD 172 searches for the minimum weight path to the leaf indicating “1”.

  FIG. 4 is a diagram showing a case where the BDD calculation processing including the above-described distribution network configuration problem is processed by one computer (device including a processor) 18. In this case, in order to determine whether or not the constraint is satisfied, it is necessary to execute a large number of power distribution network simulators, which may take a lot of processing time.

  FIG. 5 is a diagram showing a case where the distributed memory parallel computing system 19 processes the BDD operation including the distribution network configuration problem as described above. The computing system 19 includes a master device 191 and local devices 192, 193, 194. In FIG. 5, the local devices 192, 193, 194 are called local devices 1, 2, 3, respectively. Also, the computing system 19 includes three local devices, but may include fewer than three local devices and may include more than three local devices. In the calculation system 19 of FIG. 5, the master device 191 divides the entire problem into a plurality of partial problems, assigns them to a plurality of local devices, and calculates in parallel. For example, in the distribution network configuration problem, each local device is assigned a partial problem that determines whether or not a local distribution network satisfies the geometric constraint condition (C1) and the electrical constraint condition (C2). In each local device, a distribution network is configured and a distribution network simulator is executed. If the configuration satisfies the geometric constraint condition (C1) and the electrical constraint condition (C2), the master device 191 has a configuration related to the configuration. Send information. There may be a plurality of partial problems assigned to each local device or one. The master device 191 receives the configuration satisfying the geometric constraints (C1) and the electrical constraints (C2) sent from the local devices 191, 192, 193, and creates the entire BDD. Then, the master device 191 selects a BDD that represents a configuration that satisfies the condition (C-3).

  In general, for each subproblem, there are many configurations that satisfy the geometric constraint condition (C1) and the electrical constraint condition (C2), so the amount of data communication between the local device and the master device is large. Therefore, the communication time, which is the time required for this, may increase.

  FIG. 6 is a diagram illustrating an outline of parallel processing according to the first embodiment. More specifically, FIG. 6 is a diagram illustrating a case in which a BDD calculation process including a distribution network configuration problem is processed by the distributed memory parallel computing system 20. The computing system 20 includes a master device 201 and local devices 202, 203, and 204. In FIG. 6, the local devices 202, 203, and 204 are called local devices 1, 2, and 3, respectively. Also, the computing system 20 includes three local devices, but may include fewer than three local devices and may include more than three local devices.

  In the calculation system 20 of FIG. 6, the master device 201 divides the entire problem into a plurality of partial problems, assigns them to a plurality of devices, and calculates in parallel. At this time, a plurality of partial problems are assigned to one local device. A plurality of partial problems may be assigned to the master device, or one partial problem may be assigned.

  For example, the entire problem Q is obtained by performing an AND operation on the sub-problems A, B, C, D, E, F, G, H as Q = A, B, C, D, E, F, G, H. Shall be obtained as a result of application. Then, the master device 201 sets the partial problems A and B to the local device 202, the partial problems C and D to the local device 203, the partial problems E and F to the local device 204, and the partial problems G and H to the master device 201 itself. Assign to. Each device 201 to 204 represents a solution satisfying the geometric constraint condition (C1) and the electrical constraint condition (C2) with respect to the assigned subproblem in BDD. Hereinafter, the “solution of the partial problem” may mean a solution satisfying the geometric constraint condition (C1) and the electrical constraint condition (C2).

  The local devices 202 to 204 perform an AND operation between BDDs representing solutions to a plurality of given subproblems, and send information about the resulting BDD to the master device 201. For example, partial problems A and B are assigned to the local device 202. For these problems, a solution satisfying the geometric constraint condition (C1), the electrical constraint condition (C2), and the condition (C-3) is represented by BDD, and further subjected to an AND operation, and the subproblem (A · B To create a BDD representing the solution to. Here, a solution that locally satisfies the optimization condition (C-3) is represented by BDD. However, when a search for a solution that locally satisfies the optimization condition (C-3) cannot be performed, a geometric constraint is imposed. The solution may satisfy the condition (C1) and the electrical constraint condition (C2). Then, information regarding the BDD representing the solution to the partial problem (A / B) is sent to the master device 201. First, the master device 201 creates a BDD representing a solution to the partial problem (G · H). Further, in the master device 201, a BDD representing a solution to the subproblems (A · B), (C · D), and (E · F) sent from the local devices 202 to 204, and a subproblem (G · H) Perform an AND operation between BDDs representing solutions. Furthermore, the master device 201 obtains a BDD representing a configuration that satisfies the condition (C-3) globally.

  In this way, when the entire problem Q is calculated by a plurality of computers (devices) by BDD, a subproblem is assigned to each computer, and by communicating a BDD representing a solution of the subproblem assigned in each computer, An operation method and apparatus are provided that reduce processing time and speed up BDD operations.

<< Parallel processing unit for binary decision graph >>
FIG. 7A is a diagram illustrating an example of functional blocks of the master device 201, and FIG. 7B is a diagram illustrating an example of functional blocks of the local device 202 for performing parallel processing according to the present embodiment. The local devices 203 and 204 have the same or similar functional blocks as the local device 202.

  The master device 201 includes a (master) input / output control unit 2011, a problem storage unit 2012, a partial problem division unit 2013, a (master) BDD storage unit 2014, a (master) BDD operation unit 2015, and a (master) constraint satisfaction check unit 2016. Including.

  The input / output control unit 2011 controls data exchange with a local device connected to the master device 201. In addition, when the master device 201 is connected to an input device such as a keyboard for inputting a problem, data is exchanged with the input device. For example, the input / output control unit 2011 receives the distribution network configuration problem Q = A, B, C, D, E, F, G, and H as described above.

  In addition, the input / output control unit 2011 outputs a partial problem divided by the partial problem dividing unit 2013 and assigned to each local device as described later.

  Further, the input / output control unit 2011 receives the BDD representing the solution of the partial problem obtained by each local device, and stores it in the BDD storage unit 2014.

  Further, the input / output control unit 2011 may output a solution to the overall problem obtained by the BDD operation unit 2015 to an output device such as a display or a printer.

  The problem storage unit 2012 stores the combination problem Q received via the input / output control unit 2011.

  The sub-problem dividing unit 2013 divides the given problem Q into sub-problems that can be calculated independently. For example, in the case of distribution network configuration problem Q = A, B, C, D, E, F, G, H, it is divided into eight partial problems A, B, C, D, E, F, G, H.

  As a method of constructing the partial problem, for example, the entire problem Q can be divided by an AND operation as described above, but may be divided by an OR operation such as Q = A + B + C. When the partial problem is configured by dividing the whole problem by the OR operation, the AND operation may be replaced with the OR operation in the following description.

  Further, as described above, in the distribution network configuration problem, the entire distribution network can be divided into components that can partially calculate the loss. Of course, the loss may not be calculated independently for each component. In this way, whether the solution of each sub-problem satisfies the geometric constraint condition (C1), the electrical constraint condition (C2), and the condition (C-3) of the above conditions, the geometric constraint condition (C1) and the electrical Depending on whether only the conditional constraint (C2) is satisfied, the processing of the BDD operation unit 2015 described later may be slightly different from the following description.

  Further, the partial problem dividing unit 2013 assigns the divided partial problems to the master device or the local device. For example, the partial problems A and B are allocated to the local device 202, the partial problems C and D are allocated to the local device 203, the partial problems E and F are allocated to the local device 204, and the partial problems G and H are allocated to the master device 201 itself.

  The partial problems G and H assigned to the master device 201 itself by the partial problem division unit 2013 are sent to the BDD operation unit 2015.

  The BDD storage unit 2014 displays a BDD that represents a solution of the subproblem obtained by each local device input to the input / output control unit 2011 or a BDD that represents a solution of the subproblem obtained by the constraint satisfaction check unit 2016 described later. Store.

  The BDD operation unit 2015 repeats contraction from the binary tree graph for the subproblems G and H allocated to this device, and obtains BDD.

  The BDD operation unit 2015 performs an AND operation between the BDDs obtained for the partial problems G and H, and generates a BDD representing a solution to the partial problem (G · H).

  Further, the BDD operation unit 2015 uses the BDD stored in the BDD storage unit 2014 to obtain a solution to the entire problem Q. For example, BDDs representing solutions to subproblems (A · B), (C · D), and (E · F) sent from the local devices 202 to 204 and BDDs representing solutions to the subproblem (G · H) The BDD representing the configuration that satisfies the condition (C-3) is obtained.

  The constraint satisfaction check unit 2016 checks whether the BDD generated by the BDD operation unit 2015 satisfies the geometric constraint condition (C1), the electrical constraint condition (C2), and the condition (C-3). A BDD that satisfies these conditions is selected. Here, the solution that locally satisfies the geometric constraint condition (C1), the electrical constraint condition (C2), and the optimization condition (C-3) is represented by BDD. In the case where a locally satisfying solution cannot be searched, a solution satisfying the geometric constraint condition (C1) and the electrical constraint condition (C2) may be used.

  The local device 202 includes a (local) input / output control unit 2021, a partial problem storage unit 2022, a (local) BDD storage unit 2023, a (local) BDD operation unit 2024, and a (local) constraint satisfaction check unit 2025.

  The input / output control unit 2021 exchanges data with the master device 201. For example, the input / output control unit 2021 receives the subproblem assigned to the roman device 202, and obtains information related to the BDD that represents the solution of the subproblem obtained by the constraint satisfaction check unit 2025 described later and stored in the BDD storage unit 2014. Output to the master device 201.

  The BDD storage unit 2023 stores a BDD representing a solution of the partial problem obtained by the constraint satisfaction check unit 2025 described later.

  The BDD operation unit 2024 repeats contraction from the binary tree graph for the subproblems A and B assigned to the present device, and obtains BDD.

  Also, the BDD operation unit 2024 performs an AND operation between the BDDs obtained for the partial problems A and B, and generates a BDD representing a solution to the partial problem (A · B).

  The constraint satisfaction check unit 2025 checks whether the BDD generated by the BDD operation unit 2015 satisfies the geometric constraint condition (C1), the electrical constraint condition (C2), and the condition (C-3). A BDD that satisfies these conditions is selected. Also here, the solution that locally satisfies the geometric constraint condition (C1), the electrical constraint condition (C2), and the optimization condition (C-3) is represented by BDD, but the optimization condition (C-3) is In the case where a locally satisfying solution cannot be searched, a solution satisfying the geometric constraint condition (C1) and the electrical constraint condition (C2) may be used.

  Although not shown, the local devices 203 and 204 have the same or similar configuration as the local device 202. For example, the local device 203 includes an input / output control unit 2031, a partial problem division unit 2032, a BDD storage unit 2033, a BDD operation unit 2034, and a constraint satisfaction check unit 2035, which are an input / output control unit 2021 and a partial problem storage unit, respectively. 2022, the BDD storage unit 2023, the BDD operation unit 2024, and the constraint satisfaction check unit 2025 have the same or similar configuration and / or function.

FIG. 8 is a diagram for explaining communication between the master device 201 and the local device 202.
Partial problems A and B are sent from the master device 201 to the local device 202. In addition, information regarding the BDD representing the solution of the partial problem (A / B) is sent from the local device 202 to the master device 201.

  FIG. 9 is a diagram illustrating an example of a BDD representing a solution of a partial problem (A / B). Information relating to the BDD shown in FIG. 9 is sent from the local device 202 to the master device 201 in the form shown in Table 2.

  Each row in Table 2 includes the name of a certain node, the nodes a, b, c, etc. of FIG. 9, the node that goes to “0” at that node, and the node that goes to “1” at that node. For example, the first row of Table 2 represents the lower left leaf “0” in FIG. 9, and the second row represents the lower right leaf “1”.

  The third row of Table 2 is the top node a. When it is "0", it goes to the fourth node or node c. When it is "1", it goes to the third node or node b. Represents. Thus, when Table 2 is sent as data, the BDD of FIG. 9 can be reconstructed.

  FIG. 10 is a configuration diagram illustrating an example of a configuration of a parallel calculation device for a binary decision graph. The parallel computation device for the binary decision graph can be realized as the general-purpose computer 500.

  The computer 500 includes an MPU 502, ROM 504, RAM 506, hard disk device 508, input device 510, display device 512, interface device 514, and recording medium drive device 516. These components are connected via a bus line 520, and various data can be exchanged under the management of the MPU 502.

  An MPU (Micro Processing Unit) 502 is an arithmetic processing unit that controls the operation of the entire computer 500, and functions as a control processing unit of the computer 500.

  A ROM (Read Only Memory) 504 is a read-only semiconductor memory in which a predetermined basic control program is recorded in advance. The MPU 502 reads out and executes this basic control program when the computer 500 is activated, thereby enabling operation control of each component of the computer 500.

  A RAM (Random Access Memory) 506 is a semiconductor memory that can be written and read at any time and used as a working storage area as necessary when the MPU 502 executes various control programs.

  The hard disk device 508 is a storage device that stores various control programs executed by the MPU 502 and various data. The MPU 502 reads out and executes a predetermined control program stored in the hard disk device 508, thereby performing various control processes described later.

  The input device 510 is, for example, a mouse device or a keyboard device, and when operated by a user of the system of FIG. Send to.

The display device 512 is, for example, a liquid crystal display, and displays various texts and images according to display data sent from the MPU 502.
The interface device 514 manages the exchange of various information with various devices connected to the computer 500.

  The recording medium driving device 516 is a device that reads various control programs and data recorded on the portable recording medium 518. The MPU 502 can read out and execute a predetermined control program recorded on the portable recording medium 218 via the recording medium driving device 516, thereby performing various control processes described later. As the portable recording medium 218, for example, a flash memory equipped with a USB (Universal Serial Bus) standard connector, a CD-ROM (Compact Disc Read Only Memory), a DVD-ROM (Digital Versatile Disc Only Only). and so on.

  In order to configure a binary calculation graph parallel arithmetic apparatus using such a computer 500, for example, a control program for causing the MPU 502 to perform the processing in each processing unit described above is created. The created control program is stored in advance in the hard disk device 508 or the portable recording medium 518. Then, a predetermined instruction is given to the MPU 502 to read and execute the control program. By doing so, the MPU 502 provides the functions of the binary computation graph parallel computing device.

<< Processing of Parallel Processing Unit for Binary Decision Graph >>
With reference to FIG. 11, the process of the parallel arithmetic unit 20 of the binary decision graph will be described. In FIG. 11, the processing sequence of the master device 201 and the local devices 202 and 203 is shown, but the local device 204 may be further included as shown in FIG.

  In the following, as in the distribution network configuration problem described above, for each subproblem, a solution satisfying the geometric constraint condition (C1), the electrical constraint condition (C2), and the condition (C-3) of the above conditions is obtained. Assume a configurable case. Hereinafter, such a partial problem may be referred to as a “subproblem that can be calculated independently”. In this case, one solution that satisfies the local optimization condition (C-3) is obtained for each subproblem. However, as described above, it is possible to modify the following processing for other cases.

  First, when processing is started, in S101, the partial problem dividing unit 2013 of the master device 201 divides the entire problem into partial problems that can be calculated independently. It is assumed that the entire problem Q is obtained as a result of performing an AND operation of the partial problems A, B, C, and D as Q = A · B · C · D. In S101, the partial problem division unit 2013 of the master device 201 divides the overall problem Q into partial problems A, B, C, and D. In S101, the sub-problem dividing unit 2013 of the master device 201 assigns the divided sub-problems to the local devices 202 and 203, respectively. For example, partial problems A and B are assigned to local device 202 and partial problems C and D are assigned to local device 203.

  In next step S <b> 102, the input / output control unit 2011 of the master device 201 transmits the partial problem to the local devices 202 and 203. For example, the partial problems A and B are transmitted to the local device 202, and the partial problems C and D are transmitted to the local device 203.

  In step S <b> 103, the input / output control unit 2021 of the local device 202 receives partial problems, for example, partial problems A and B, from the master device 201. In S103, the local device 202 may store the received partial problem in the partial problem storage unit 2022.

  In step S <b> 104, the input / output control unit 2031 of the local device 203 receives partial problems, for example, partial problems C and D, from the master device 201. In S104, the local device 203 may store the received partial problem in the partial problem storage unit 2032. When the process of S104 ends, the process proceeds to S108.

  In step S <b> 105, the BDD operation unit 2024 of the local device 202 generates all of the partial problem solutions received from the master device 201 as BDDs. For example, all the solutions of the partial problems A and B are generated as BDD. At this time, the constraint satisfaction check unit 2025 checks whether the generated BDD satisfies the constraint condition. In S105, the BDD operation unit 2024 of the local device 202 may store the generated BDD in the BDD storage unit 2023. When the process of S105 ends, the process proceeds to S106.

  In S106, if there are a plurality of BDDs, the BDD operation unit 2024 of the local device 202 makes one by AND operation. For example, if there is a BDD representing the subproblems A and B, an AND operation is performed on the BDDs as shown in FIG. 2A to generate a BDD representing the solution of the subproblem (A · B). In S106, the BDD operation unit 2024 of the local device 202 stores the generated BDD in the BDD storage unit 2023. When the process of S106 ends, the process proceeds to S107.

  In step S <b> 107, the input / output control unit 2021 of the local device 202 transmits the BDD generated in step S <b> 106 to the master device 201. When the process of S107 ends, the process proceeds to S111.

  In S108 following S104, the BDD operation unit 2034 of the local device 203 generates all of the partial problem solutions received from the master device 201 as BDDs. At this time, the constraint satisfaction check unit 2035 checks whether the generated BDD satisfies the constraint condition. For example, all the solutions of the partial problems C and D are generated as BDD. In S108, the BDD operation unit 2034 of the local device 203 may store the generated BDD in the BDD storage unit 2033. When the process of S108 ends, the process proceeds to S109.

  In S109, if there are a plurality of BDDs, the BDD operation unit 2034 of the local device 203 unites them by AND operation. For example, if there is a BDD representing the subproblems C and D, an AND operation is performed on the BDDs as shown in FIG. 2A to generate a BDD representing the solution of the subproblem (C · D). In S109, the BDD operation unit 2034 of the local device 203 stores the generated BDD in the BDD storage unit 2033. When the process of S109 ends, the process proceeds to S110.

  In S110, the input / output control unit 2031 of the local device 203 transmits the BDD generated in S109 to the master device 201. When the processing of S110 ends, the process proceeds to S111.

  In step S <b> 111, the input / output control unit 2011 of the master device 201 receives the BDD representing the solution of the partial problem sent from the local devices 202 and 203. The received BDD may be stored in the BDD storage unit 2014. The BDD operation unit 2015 performs an AND operation on the BDD representing the solution of the partial problem sent from the local devices 202 and 203, and generates a BDD representing the solution of the entire problem Q = A · B · C · D. At this time, the constraint satisfaction check unit 2016 may check whether or not the generated BDD satisfies the above conditions (C-1) to (C-3) if the generated BDD is a constraint condition, for example, a distribution network configuration problem. If a solution to the overall problem Q is obtained, the process ends.

  In the processing shown in FIG. 11, the partial problem is not assigned to the master device 201, but the partial problem may be assigned to the master device 201. In that case, the master device 201 performs the processing of S105 to S106 or S108 to S109, and creates a BDD representing the solution of the assigned subproblem. In step S <b> 111, the BDD operation unit 2014 of the master device 201 performs an AND operation on the BDD that represents the solution of the subproblem sent from the local devices 202 and 203 and the BDD that represents the solution of the subproblem obtained by the master device 201. Create a BDD that represents the solution of the overall problem.

  Thus, the communication time can be shortened because the constraint satisfaction solution is compressed and transmitted by BDD. When a BDD is divided and a partial problem is assigned to a plurality of computers for processing, a parallel operation method is provided that reduces the processing time by reducing the communication time, for example, while reducing the possibility of memory shortage.

<Second Embodiment>
A parallel computation device and method for a binary decision graph according to the first embodiment will be described with reference to FIGS.

<< General description >>
In this embodiment, in a system composed of a master device and a plurality of local devices, a constraint satisfaction problem is divided into a plurality of subproblems, and a binary decision graph (BDD) is constructed for each subproblem from the constraint conditions. In this method, the master device assigns a plurality of subproblems to a plurality of local devices, and each local device is a solution of a plurality of subproblems assigned. Then, a solution satisfying the constraints is constructed as a plurality of BDDs, and each local device takes a logical product of at least two logical products (AND operations) of the plurality of BDDs using the obtained BDDs as a master device. The BDD including the BDD obtained so that the size of the BDD does not exceed the sum of the sizes of the BDD before taking the logical product is transmitted, and The device receives a BDD that corresponds to the solution of partial problems, parallel operation method to obtain a solution of the constraint satisfaction problem by taking a logical product of them and, parallel operation device is provided using the method.

  FIG. 12 is a diagram illustrating an outline of parallel processing according to the second embodiment. More specifically, FIG. 12 is a diagram illustrating a case in which a BDD calculation process including a distribution network configuration problem is processed by the distributed memory type parallel calculation system 30. The computing system 30 includes a master device 301 and local devices 302, 303, and 304. In FIG. 12, the local devices 302, 303, and 304 are called local devices 1, 2, and 3, respectively. Also, the computing system 30 includes three local devices, but may include fewer than three local devices and may include more than three local devices.

  In the calculation system 30 of FIG. 12, the master device 301 divides the entire problem into a plurality of partial problems, assigns them to a plurality of devices, and calculates in parallel. At this time, a plurality of partial problems are assigned to one local device. A plurality of partial problems may be assigned to the master device, or one partial problem may be assigned.

  The calculation system 30 of FIG. 12 differs from the calculation system 20 of FIG. 6 in that (i) the local devices 302, 303, and 304 generate BDDs representing solutions of a plurality of assigned subproblems, and a plurality of BDDs are generated. When performing an AND operation, a comparison is made between the sum of the sizes of a plurality of BDDs and the size of a BDD obtained by performing the AND operation, and (ii) a sum of the sizes of a plurality of BDDs is obtained by performing an AND operation. If the size of the BDD obtained by performing the AND operation becomes larger than the sum of the sizes of the plurality of BDDs, the AND operation is stopped, and (iii) the BDD obtained by performing the AND operation. If the size is greater than the sum of the sizes of multiple BDDs, the local device sends multiple BDDs representing solutions of multiple partial problems to the master device.

  By configuring the calculation system 30 as described above, communication overhead is determined by determining a place (a device including a processor) where the operation is performed so that the BDD to be communicated is reduced or the entire processing time is reduced. Can be reduced. As a result, the overall calculation time can be reduced by parallelization.

<< Parallel processing unit for binary decision graph >>
The master device 301 in FIG. 12 has the same or similar configuration as the master device 201 of the previous embodiment. That is, the master device 301 includes an input / output control unit 3011, a problem storage unit 3012, a partial problem division unit 3013, a BDD storage unit 3014, a BDD operation unit 3015, and a constraint satisfaction check unit 3016 (not shown). These are the same as the input / output control unit 2011, the problem storage unit 2012, the partial problem division unit 2013, the BDD storage unit 2014, the BDD operation unit 2015, and the constraint satisfaction check unit 2016 of the master device 201 shown in FIG. It has a similar configuration and / or function.

  FIG. 13 is a functional block diagram of the local device 302 used in the computing system 30 of this embodiment. FIG. 13 shows functional blocks of the local device 302, which has the same or similar configuration of the local devices 303 and 304 of FIG.

  The local device 302 illustrated in FIG. 13 includes an input / output control unit 3021, a partial problem division unit 3022, a BDD storage unit 3023, a BDD operation unit 3024, a BDD size calculation unit 3025, a BDD size comparison unit 3026, and a constraint satisfaction check unit. 3027.

  The input / output control unit 3021 exchanges data with the master device 301. For example, the input / output control unit 3021 receives the partial problem assigned to the local device 302, and outputs to the master device 301 information related to the BDD that represents the solution of the partial problem assigned to the local device 302. When a plurality of subproblems are assigned to the local device 302, information regarding the BDD representing individual solutions of the plurality of subproblems may be output to the master device 301, or AND between BDDs representing the solutions of the plurality of problems. Information regarding the BDD obtained by performing the calculation may be output to the master device 301. When generating the BDD, the BDD is generated while checking that the constraint satisfaction check unit 3025 described later satisfies the constraint condition.

  The BDD storage unit 3023 stores BDDs representing solutions for a plurality of problems. The BDD storage unit 3023 may store BDDs obtained by performing an AND operation between BDDs that represent solutions to a plurality of problems.

  The BDD operation unit 3024 repeats contraction from the binary tree graph for subproblems assigned to this device, for example, subproblems A and B, to obtain BDDs.

  Further, the BDD operation unit 3024 performs an AND operation between the BDDs obtained for the partial problems A and B, and generates a BDD representing a solution to the partial problem (A · B).

  The BDD size calculation unit 3025 calculates the size of the BDD generated by the BDD calculation unit 3024. The BDD size may be the number of nodes.

  The BDD size comparison unit 3026 compares the sizes of a plurality of BDDs. For example, the sum of the BDD sizes representing the solutions obtained for the subproblems A and B is compared with the size of the BDD representing the solution for the subproblem (A · B).

  The constraint satisfaction check unit 3026 checks whether the BDD generated by the BDD operation unit 3024 satisfies the geometric constraint condition (C1), the electrical constraint condition (C2), and the condition (C-3). Also here, the solution that locally satisfies the geometric constraint condition (C1), the electrical constraint condition (C2), and the optimization condition (C-3) is represented by BDD, but the optimization condition (C-3) is In the case where a locally satisfying solution cannot be searched, a solution satisfying the geometric constraint condition (C1) and the electrical constraint condition (C2) may be used.

  The local device 302 described above compares the size of the BDD representing the solution obtained for each of the subproblems A and B with the size of the BDD representing the solution for the subproblem (A · B). Although the smaller one is configured to be transmitted to the master device 301, when the partial problem can be divided into smaller partial problems, the information regarding the BDD is combined in such a way that the size of the BDD to be transmitted becomes as small as possible. It may be transmitted to the master device 301.

<< Processing of Parallel Processing Unit for Binary Decision Graph >>
With reference to FIG. 14, the process of the parallel arithmetic unit 30 of the binary decision graph will be described. In FIG. 14, the processing sequence of the master device 301 and the local devices 302 and 303 is shown, but the local device 304 may be further included as shown in FIG.

  In the following, as in the distribution network configuration problem described above, for each subproblem, a solution satisfying the geometric constraint condition (C1), the electrical constraint condition (C2), and the condition (C-3) of the above conditions is obtained. Assume a configurable case. In this case, one solution that satisfies the local optimization condition (C-3) is obtained for each subproblem. However, as described above, it is possible to modify the following processing for other cases.

  First, when the process is started, the sub-problem dividing unit 3013 of the master device 301 divides the entire problem into sub-problems that can be calculated independently in S201. It is assumed that the entire problem Q is obtained as a result of performing an AND operation of the partial problems A, B, C, and D as Q = A · B · C · D. In S201, the partial problem dividing unit 3013 of the master device 301 divides the entire problem Q into partial problems A, B, C, and D. In S201, the sub-problem dividing unit 3013 of the master device 301 allocates the divided sub-problems to the local devices 302 and 303, respectively. For example, partial problems A and B are assigned to local device 302 and partial problems C and D are assigned to local device 303.

  In next step S <b> 202, the input / output control unit 3011 of the master device 301 transmits the partial problem to the local devices 302 and 303. For example, the partial problems A and B are transmitted to the local device 302, and the partial problems C and D are transmitted to the local device 303.

  In step S <b> 203, the input / output control unit 3021 of the local device 302 receives partial problems, for example, partial problems A and B, from the master device 301. In S203, the local device 302 may store the received partial problem in the partial problem storage unit 3022. When the process of S203 ends, the process proceeds to S205.

  In step S <b> 204, the input / output control unit 3031 of the local device 303 receives partial problems, for example, partial problems C and D, from the master device 301. In S204, the local device 303 may store the received partial problem in the partial problem storage unit 3032. When the process of S204 ends, the process proceeds to S209.

  In step S <b> 205, the BDD operation unit 3024 of the local device 302 generates all of the partial problem solutions received from the master device 301 as BDDs. For example, all the solutions of the partial problems A and B are generated as BDD. At this time, the constraint satisfaction check unit 3027 checks whether the generated BDD satisfies the constraint condition. In S205, the BDD operation unit 3024 of the local device 302 may store the generated BDD in the BDD storage unit 3023. When the processing of S205 ends, the process proceeds to S206.

  In S206, the BDD size calculation unit 3025 of the local device 302 calculates the BDD representing the solution of the partial problem generated in S205, for example, the BDD size sum S1 representing the solutions of the partial problems A and B. When the process of S206 ends, the process proceeds to S207.

  In S207, if there are a plurality of BDDs generated in S206, the BDD operation unit 3024 of the local device 302 performs an AND operation between the BDDs to make one. For example, if there is a BDD representing the subproblems A and B, an AND operation is performed on the BDDs as shown in FIG. 2A to generate a BDD representing the solution of the subproblem (A · B). In this case, the constraint satisfaction check unit 3027 may check whether or not the generated BDD satisfies the above conditions (C-1) to (C-3) if the generated BDD is a constraint condition, for example, a distribution network configuration problem. In S207, the BDD size comparison unit 3026 instructs the BDD operation unit 3024 to stop the process when the BDD size becomes S1 obtained in S206 in the process of uniting the BDDs. put out. In S207, the BDD operation unit 3024 of the local device 302 stores the generated BDD in the BDD storage unit 3023. When the processing of S207 ends, the process proceeds to S208.

  In step S <b> 208, the input / output control unit 3021 of the local device 302 transmits the BDD generated in step S <b> 207 to the master device 301. For example, if the sum S1 of the sizes of the two BDDs representing the solutions of the subproblems A and B is smaller than the size of the BDD representing the solution of the subproblem (A · B), the input / output control unit 3021 of the local device 302 Information regarding two BDDs representing the solutions of the partial problems A and B is transmitted to the master device 301. If the sum S1 of the sizes of the two BDDs representing the solutions of the partial problems A and B is larger than the size of the BDD representing the solution of the partial problem (A · B), the input / output control unit 3021 of the local device 302 Information related to the BDD representing the solution of (A · B) is transmitted to the master device 301. When transmitting information related to a plurality of BDDs, an operation to be performed between the plurality of BDDs, for example, information related to an AND operation is also transmitted together. When the processing of S208 ends, the process proceeds to S213.

  In S209 following S204, the BDD operation unit 3034 of the local device 303 generates all of the partial problem solutions received from the master device 301 as BDDs. For example, all the solutions of the partial problems C and D are generated as BDD. At this time, the constraint satisfaction check unit 3037 checks whether or not the generated BDD satisfies the above conditions (C-1) to (C-3) if the generated BDD is a constraint condition, for example, a distribution network configuration problem. In S209, the BDD operation unit 3034 of the local device 303 may store the generated BDD in the BDD storage unit 3033. When the process of S209 ends, the process proceeds to S210.

  In S210, the BDD size calculator 3035 of the local device 303 calculates a BDD representing the solution of the partial problem generated in S209, for example, the size sum S2 of BDD representing the solutions of the partial problems C and D. When the processing of S210 ends, the process proceeds to S211.

  In S211, if there are a plurality of BDDs generated in S210, the BDD operation unit 3034 of the local device 303 performs an AND operation between the BDDs to make one. For example, if there is a BDD representing partial problems C and D, an AND operation is performed on the BDDs as shown in FIG. 2A to generate a BDD representing the solution of the partial problem (C · D). At this time, the constraint satisfaction check unit 3037 may check whether the generated BDD satisfies the constraint condition. In S211, the BDD size comparison unit 3036 instructs the BDD calculation unit 3034 to stop the process when the BDD size becomes S2 obtained in S210 in the process of uniting the BDDs. put out. In S211, the BDD operation unit 3034 of the local device 303 stores the generated BDD in the BDD storage unit 3033. When the process of S211 is completed, the process proceeds to S212.

  In step S <b> 212, the input / output control unit 3031 of the local device 303 transmits the BDD generated in step S <b> 211 to the master device 301. For example, if the sum S2 of the sizes of the two BDDs representing the solutions of the subproblems C and D is smaller than the size of the BDD representing the solution of the subproblem (C · D), the input / output control unit 3031 of the local device 303 Information regarding two BDDs representing solutions of the partial problems C and D is transmitted to the master device 301. If the sum S2 of the sizes of the two BDDs representing the solutions of the subproblems C and D is larger than the size of the BDD representing the solution of the subproblem (C · D), the input / output control unit 3031 of the local device 303 Information regarding the BDD representing the solution of (C · D) is transmitted to the master device 301. When transmitting information related to a plurality of BDDs, an operation to be performed between the plurality of BDDs, for example, information related to an AND operation is also transmitted together. When the process of S212 ends, the process proceeds to S213.

  In step S <b> 213, the input / output control unit 3011 of the master device 301 receives the BDD that represents the solution to the partial problem transmitted from the local devices 302 and 303. The received BDD may be stored in the BDD storage unit 3014. When BDDs representing solutions of a plurality of partial problems are separately sent from the local devices 302 and 303, the BDD calculation unit 3015 performs a calculation between them. In FIG. 14, such a process is called a type-specified BDD operation. Further, the BDD operation unit 3015 performs an AND operation on one BDD that represents a solution of a plurality of subproblems assigned to each local device, and obtains a BDD that represents the solution of the entire problem Q = A · B · C · D. Generate. At this time, the constraint satisfaction check unit 3027 may check whether the generated BDD satisfies the constraint condition. If a solution to the overall problem Q is obtained, the process ends.

<< Modification >>
A modification of the second embodiment will be described with reference to FIGS.

  In the above embodiment, each local device performs the following processing. First, all the sets of solutions that satisfy the constraints of the assigned subproblem are constructed as BDDs. At that time, whether or not the solution candidate satisfies the constraint is calculated by simulation or the like. If there are a plurality of partial problems assigned to the local device, an AND operation between BDDs representing solutions is performed. If the BDD size becomes equal to the sum of the BDD sizes representing the solutions of the individual subproblems during the AND operation, the operation is stopped halfway and the BDD being built is discarded. When the AND operation is completed, all the BDDs representing the solutions of the individual subproblems are discarded, and the BDD obtained by the AND operation is the result.

  On the other hand, in this modification, each local device performs the following processing. If there are a plurality of partial problems assigned to the local device, a time Ta required for communication of information related to BDD obtained by performing an AND operation thereof and a time Tb for communication while BDD is estimated, and Ta is smaller Then, an AND operation of BDDs representing solutions of a plurality of subproblems is taken, and the BDDs combined into one result are obtained.

  As described above, in this modification, the information about the BDD representing each solution of the plurality of partial problems from the local device to the master device is not based on the size of the BDD but the size of the communication time for communicating information about the BDD. Then, it is determined whether or not to transmit a BDD obtained by calculating a BDD representing a solution of a plurality of subproblems, for example, performing an AND operation.

  In general, the communication time includes a portion proportional to the number of BDD nodes and a latency portion. For example, in communication within a device, the communication time can be estimated approximately by ((number of nodes) −2) × (capacity per node) / (throughput) + latency. ((Number of nodes) −2) is attributed to the two terminal nodes. For example, the capacity per node is 12 bytes, the throughput is 300 Kbytes, and the latency is 0.001 milliseconds. In inter-device communication, latency is greater than in intra-device communication. For example, it may be 0.1 milliseconds.

  FIG. 15 is a diagram illustrating an example of functional blocks of the local device 402 for performing a modification of parallel processing according to the second embodiment.

  The local device 402 shown in FIG. 15 may be used in the computing system 30 instead of the local device 302 shown in FIG.

  The local device 402 shown in FIG. 15 includes an input / output control unit 4021, a partial problem division unit 4022, a BDD storage unit 4023, a BDD operation unit 4024, a communication time estimation unit 4025, a communication time comparison unit 4026, and a constraint satisfaction check unit. 4027 included. For the input / output control unit 4021, the partial problem division unit 4022, the BDD storage unit 4023, the BDD calculation unit 4024, and the constraint satisfaction check unit 4027, the input / output control unit 3021 of the local device 302 shown in FIG. Since the configuration and / or function is the same as or similar to that of the unit 3022, the BDD storage unit 3023, the BDD operation unit 3024, and the constraint satisfaction check unit 3027, description thereof will be omitted.

  The communication time estimation unit 4025 estimates a communication time for communicating the BDD generated by the BDD calculation unit 4024.

  The communication time comparison unit 4026 compares the communication time for communicating each of the plurality of BDDs. For example, the sum of communication times for communicating BDDs representing solutions obtained for subproblems A and B and the communication time for communicating BDDs representing solutions for subproblems (A · B) Compare.

  FIG. 16 is a diagram illustrating processing of the parallel computation device 30 of the binary decision graph configured by the master device 301, the local device 402, and the local device 403.

  S301 is the same process as S201 of FIG. However, the sub-problem dividing unit 3013 of the master device 301 assigns the divided sub-problems to the local devices 402 and 403, respectively. For example, the partial problems A and B are assigned to the local device 402, and the partial problems C and D are assigned to the local device 403.

  In next step S <b> 302, the input / output control unit 3011 of the master device 301 transmits the partial problem to the local devices 402 and 403. For example, the partial problems A and B are transmitted to the local device 402, and the partial problems C and D are transmitted to the local device 403.

  In step S <b> 303, the input / output control unit 4021 of the local device 402 receives partial problems such as partial problems A and B from the master device 301. In S303, the local device 402 may store the received partial problem in the partial problem storage unit 4022. When the process of S303 ends, the process proceeds to S305.

  In step S <b> 304, the input / output control unit 4031 of the local device 403 receives partial problems, for example, partial problems C and D, from the master device 301. In S304, the local device 403 may store the received partial problem in the partial problem storage unit 4032. When the process of S304 ends, the process proceeds to S309.

  In step S <b> 203, the BDD operation unit 4024 of the local device 402 generates all of the partial problem solutions received from the master device 301 as BDDs. For example, all the solutions of the partial problems A and B are generated as BDD. At this time, the constraint satisfaction check unit 4027 checks whether the generated BDD satisfies the constraint condition. In S305, the BDD operation unit 4024 of the local device 402 may store the generated BDD in the BDD storage unit 4023. When the processing of S305 ends, the process proceeds to S306.

  In S306, the communication time estimation unit 4025 of the local device 302 calculates a communication time T1 necessary for communicating the BDD representing the solution of the partial problem generated in S205, for example, the BDD representing the solutions of the partial problems A and B. When the process of S306 ends, the process proceeds to S307.

  In S307, if there are a plurality of BDDs generated in S303, the BDD operation unit 4024 of the local device 402 performs an AND operation between the BDDs to make one. For example, if there is a BDD representing the subproblems A and B, an AND operation is performed on the BDDs as shown in FIG. 2A to generate a BDD representing the solution of the subproblem (A · B). At this time, the constraint satisfaction check unit 4027 may check whether the generated BDD satisfies the constraint condition. In S307, the communication time comparison unit 4026 cancels the process when the communication time required for communicating the BDD reaches T1 obtained in S306 in the process of making one BDD. A command is issued to the BDD operation unit 4024. In S307, the BDD operation unit 4024 of the local device 302 stores the generated BDD in the BDD storage unit 4023. When the processing of S307 ends, the process proceeds to S308.

  In step S <b> 308, the input / output control unit 4021 of the local device 402 transmits the BDD generated in step S <b> 307 to the master device 301. For example, the sum T1 of the communication time required to communicate two BDDs representing the solutions of the subproblems A and B is greater than the communication time required to communicate the BDD representing the solutions of the subproblems (A and B). If it is smaller, the input / output control unit 4021 of the local device 402 transmits to the master device 301 information related to two BDDs representing the solutions of the partial problems A and B. If the sum T1 of communication times required for communicating two BDDs representing the solutions of the subproblems A and B is greater than the communication time required for communicating the BDD representing the solutions of the subproblems (A and B) The input / output control unit 4021 of the local device 402 transmits to the master device 301 information related to the BDD representing the solution of the partial problem (A / B). When transmitting information related to a plurality of BDDs, an operation to be performed between the plurality of BDDs, for example, information related to an AND operation is also transmitted together. When the processing of S308 ends, the process proceeds to S313.

  In S 309 subsequent to S 304, the BDD operation unit 4034 of the local device 403 generates all of the partial problem solutions received from the master device 301 as BDD. For example, all the solutions of the partial problems C and D are generated as BDD. At this time, the constraint satisfaction check unit 4037 checks whether the generated BDD satisfies the constraint condition. In S309, the BDD operation unit 4034 of the local device 403 may store the generated BDD in the BDD storage unit 4033. When the process of S309 ends, the process proceeds to S310.

  In S310, the BDD size calculation unit 4035 of the local device 403 calculates the sum T2 of communication time necessary for communicating the BDD representing the solution of the partial problem generated in S309, for example, the BDD representing the solutions of the partial problems C and D. To do. When the process of S310 ends, the process proceeds to S311.

  In S311, if there are a plurality of BDDs generated in S310, the BDD operation unit 4034 of the local device 403 performs an AND operation between the BDDs to make one. For example, if there is a BDD representing partial problems C and D, an AND operation is performed on the BDDs as shown in FIG. 2A to generate a BDD representing the solution of the partial problem (C · D). At this time, the constraint satisfaction check unit 4037 may check whether the generated BDD satisfies the constraint condition. In S311, the communication time comparison unit 4036 cancels the process when the communication time required for communicating the BDD reaches T2 obtained in S310 in the process of uniting the BDD. A command is issued to the BDD operation unit 4034. In S <b> 311, the BDD operation unit 4034 of the local device 403 stores the generated BDD in the BDD storage unit 4033. When the process of S311 ends, the process proceeds to S312.

  In step S <b> 312, the input / output control unit 4031 of the local device 403 transmits the BDD generated in step S <b> 311 to the master device 301. For example, the sum of communication times T2 required to communicate two BDDs representing solutions of the subproblems C and D is greater than the communication time required to communicate BDD representing the solutions of the subproblems (C · D). If it is smaller, the input / output control unit 4031 of the local device 403 transmits information about two BDDs representing the solutions of the partial problems C and D to the master device 301. If the sum T2 of communication times required for communicating two BDDs representing the solutions of the subproblems C and D is greater than the communication time required for communicating the BDD representing the solutions of the subproblems (C · D) The input / output control unit 4031 of the local device 403 transmits information related to the BDD representing the solution of the partial problem (C · D) to the master device 301. When transmitting information related to a plurality of BDDs, an operation to be performed between the plurality of BDDs, for example, information related to an AND operation is also transmitted together. When the process of S312 ends, the process proceeds to S313.

  In step S <b> 313, the input / output control unit 3011 of the master device 301 receives the BDD that represents the solution to the partial problem transmitted from the local devices 402 and 403. The received BDD may be stored in the BDD storage unit 3014. When BDDs representing solutions of a plurality of subproblems are separately sent from the local devices 402 and 403, the BDD operation unit 3015 performs an operation between them. Further, the BDD operation unit 3015 performs an AND operation on one BDD that represents a solution of a plurality of subproblems assigned to each local device, and obtains a BDD that represents the solution of the entire problem Q = A · B · C · D. Generate. At this time, the constraint satisfaction check unit 3027 may check whether the generated BDD satisfies the constraint condition. If a solution to the overall problem Q is obtained, the process ends.

Regarding the above embodiment, the following additional notes are disclosed.
(Appendix 1)
A binary decision graph processing system comprising a master device and a local device,
The master device is
A sub-problem dividing unit that divides the entire problem into a plurality of sub-problems;
A master I / O controller that transmits at least two subproblems of the plurality of subproblems to the local device and receives a binary decision graph (BDD) representing solutions of the at least two subproblems from the local device; ,
Including
The local device is
A local input / output controller that receives the at least two subproblems from the master device and transmits the one binary decision graph (BDD) representing solutions of the at least two subproblems;
A binary decision graph representing each solution of the at least two subproblems is created, and if the binary decision graph representing the respective solutions satisfies a predetermined condition, the binary decision graph represents each solution of the at least two subproblems A local BDD computing unit that computes the binary decision graphs to generate the one binary decision graph;
A local constraint satisfaction check unit that determines whether the binary decision graph generated by the local BDD calculation unit satisfies a constraint condition;
A binary decision graph processing system.
(Appendix 2)
When there are a plurality of local devices, the master device calculates binary decision graphs representing solutions of at least two partial problems sent from the local device and solves the whole problem. The binary decision graph processing system according to appendix 1, including a master BDD calculation unit that generates a binary decision graph representing
(Appendix 3)
The local device further includes
A BDD size calculation unit for calculating the sum of the sizes of the binary decision graphs representing the respective solutions of the subproblem and the size of the one binary decision graph obtained by calculation;
A BDD size comparison unit that compares the sum of the sizes of the binary decision graphs representing the respective solutions of the subproblem calculated by the BDD size calculation unit and the size of the one binary decision graph obtained by the calculation; ,
Including
The dichotomy according to appendix 1 or 2, wherein the predetermined condition is that a sum of sizes of the binary decision graphs representing respective solutions of the subproblem is larger than a size of the one binary decision graph obtained by calculation. Decision graph processing system.
(Appendix 4)
The local device further includes
Sum of communication times for communicating the binary decision graph representing each solution of the subproblem to the master device, and communication time for communicating the one binary decision graph obtained by calculation to the master device A communication time estimation unit for calculating
A sum of communication times for communicating the binary decision graph representing each solution of the partial problem calculated by the communication time estimation unit to the master device, and the one binary decision graph obtained by the calculation A communication time comparison unit for comparing communication time for communicating with the master device;
Including
The predetermined condition is that the one binary decision graph obtained by computing a sum of communication times for communicating the binary decision graph representing each solution of the partial problem to the master device is stored in the master device. The binary decision graph processing system according to appendix 1 or 2, which is longer than the communication time for communication.
(Appendix 5)
The overall problem includes a problem of deriving an output function of a logic circuit, a problem of enumerating on / off combinations of switches having restrictions on combinations, and a problem of enumerating combinations of selection or non-selection of items having restrictions on combinations. The binary decision graph processing system according to any one of appendices 1 to 4, which is a problem expressed as a calculation of a logical function.
(Appendix 6)
A binary decision graph processing method configured as a master device configured as a computer and a computer configured as a computer and processed by a local device different from the master device,
The master device divides the overall problem into a plurality of partial problems;
The master device sends at least two subproblems of the plurality of subproblems to the local device;
The local device receives the at least two subproblems from the master device;
The local device generates a binary decision graph representing a solution of each of the at least two subproblems;
The local device determines whether the generated binary decision graph satisfies a constraint condition;
When the binary decision graph representing the respective solutions satisfies a predetermined condition, the local device calculates the binary decision graphs representing the respective solutions of the partial problem and generates one binary decision graph. To do
The local device transmitting the one binary decision graph determined to satisfy the constraint condition to the master device; and the one binary decision graph representing solutions of the at least two subproblems from the local device ( Receiving BDD),
A binary decision graph processing method including:
(Appendix 7)
Further, when there are a plurality of local devices, the master device calculates binary decision graphs representing solutions of at least two partial problems of the plurality of partial problems sent from the local device, and calculates the overall problem. The parallel calculation method according to appendix 6, including generating a binary decision graph representing the solution of
(Appendix 8)
Furthermore, the local device calculates the sum of the sizes of the binary decision graphs representing the respective solutions of the subproblems and the size of the one binary decision graph obtained by calculation, and calculates the calculated subproblems. Comparing the sum of the sizes of the binary decision graphs representing the respective solutions of the one and the size of the one binary decision graph obtained by the calculation;
Including
The dichotomy according to appendix 6 or 7, wherein the predetermined condition is that a sum of sizes of the binary decision graphs representing respective solutions of the subproblem is larger than a size of the one binary decision graph obtained by calculation. Decision graph processing method.
(Appendix 8)
Further, the local device is configured to obtain a sum of communication times for communicating the binary decision graph representing each solution of the subproblem to the master device, and the one binary decision graph obtained by calculation. A communication time for communicating with the master device, and a communication time for communicating the binary decision graph representing each solution of the calculated subproblem to the master device, and the computation obtained. Comparing the communication time for communicating one binary decision graph to the master device;
Including
The predetermined condition is that the one binary decision graph obtained by computing a sum of communication times for communicating the binary decision graph representing each solution of the partial problem to the master device is stored in the master device. The binary decision graph processing method according to appendix 6 or 7, which is longer than the communication time for communication.
(Appendix 10)
The overall problem includes a problem of deriving an output function of a logic circuit, a problem of enumerating on / off combinations of switches having restrictions on combinations, and a problem of enumerating combinations of selection or non-selection of items having restrictions on combinations. The binary decision graph processing method according to any one of appendices 6 to 9, which is a problem expressed as a calculation of a logical function.

20, 30 Binary decision graph processing system 201, 301 Master device 202, 203, 204, 302, 303, 304, 402, 403 Local device 2011, 3011 (first) input / output control unit 2012 problem storage unit 2013 (first (First) BDD storage unit 2015 (first) DD operation unit 2016 (first) constraint satisfaction check unit 2021, 2031, 2041, 3021, 3031, 3041, 4021, 4031 (Second) input / output control unit 2022, 2032, 2042, 3022, 3032, 3042, 4022, 4032 (second) partial problem storage unit 2023, 2033, 2043, 3023, 3033, 3043, 4023, 4033 (second) BDD storage units 2024, 2034, 2044, 024, 3034, 3044, 4024, 4034 (Second) BDD operation unit 2025, 2035, 2045, 3027, 3037, 3047, 4027, 4037 (Second) BDD operation unit 3025, 3035, 3045 BDD size calculation unit 3026 , 3036, 3046 BDD size comparison unit 4025, 4035, 4045 Communication time estimation unit 4026, 4036, 4046 Communication time comparison unit

Claims (6)

A binary decision graph processing system comprising a master device and a local device,
The master device is
A sub-problem dividing unit that divides the entire problem into a plurality of sub-problems;
A master I / O controller that transmits at least two subproblems of the plurality of subproblems to the local device and receives a binary decision graph (BDD) representing solutions of the at least two subproblems from the local device; ,
Including
The local device is
A local input / output controller that receives the at least two subproblems from the master device and transmits the one binary decision graph (BDD) representing solutions of the at least two subproblems;
A binary decision graph representing each solution of the at least two subproblems is created, and if the binary decision graph representing the respective solutions satisfies a predetermined condition, the binary decision graph represents each solution of the at least two subproblems A local BDD computing unit that computes the binary decision graphs to generate the one binary decision graph;
A local constraint satisfaction check unit that determines whether the binary decision graph generated by the local BDD calculation unit satisfies a constraint condition;
A binary decision graph processing system.   When there are a plurality of local devices, the master device calculates binary decision graphs representing solutions of at least two partial problems sent from the local device and solves the whole problem. The binary decision graph processing system according to claim 1, further comprising a first BDD operation unit that generates a binary decision graph representing The local device further includes
A BDD size calculation unit for calculating the sum of the sizes of the binary decision graphs representing the respective solutions of the subproblem and the size of the one binary decision graph obtained by calculation;
A BDD size comparison unit that compares the sum of the sizes of the binary decision graphs representing the respective solutions of the subproblem calculated by the BDD size calculation unit and the size of the one binary decision graph obtained by the calculation; ,
Including
The predetermined condition is that a sum of sizes of the binary decision graphs representing respective solutions of the subproblem is larger than a size of the one binary decision graph obtained by calculation. Binary decision graph processing system. The local device further includes
Sum of communication times for communicating the binary decision graph representing each solution of the subproblem to the master device, and communication time for communicating the one binary decision graph obtained by calculation to the master device A communication time estimation unit for calculating
A sum of communication times for communicating the binary decision graph representing each solution of the partial problem calculated by the communication time estimation unit to the master device, and the one binary decision graph obtained by the calculation A communication time comparison unit for comparing communication time for communicating with the master device;
Including
The predetermined condition is that the one binary decision graph obtained by computing a sum of communication times for communicating the binary decision graph representing each solution of the partial problem to the master device is stored in the master device. The binary decision graph processing system according to claim 1 or 2, wherein the communication time is longer than a communication time for communication.   The overall problem includes a problem of deriving an output function of a logic circuit, a problem of enumerating on / off combinations of switches having restrictions on combinations, and a problem of enumerating combinations of selection or non-selection of items having restrictions on combinations. The binary decision graph processing system according to any one of claims 1 to 4, which is a problem expressed as a calculation of a logical function. A binary decision graph processing method configured as a master device configured as a computer and a computer configured as a computer and processed by a local device different from the master device,
The master device divides the overall problem into a plurality of partial problems;
The master device sends at least two subproblems of the plurality of subproblems to the local device;
The local device receives the at least two subproblems from the master device;
The local device generates a binary decision graph representing a solution of each of the at least two subproblems;
The local device determines whether the generated binary decision graph satisfies a constraint condition;
When the binary decision graph representing the respective solutions satisfies a predetermined condition, the local device calculates the binary decision graphs representing the respective solutions of the partial problem and generates one binary decision graph. To do
The local device transmitting the one binary decision graph determined to satisfy the constraint condition to the master device; and the one binary decision graph representing solutions of the at least two subproblems from the local device ( Receiving BDD),
A binary decision graph processing method including: