CN109522455A - The overhead method that a large amount of random access of reduction based on half external memory nomography of Swap generate - Google Patents

The overhead method that a large amount of random access of reduction based on half external memory nomography of Swap generate Download PDF

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CN109522455A
CN109522455A CN201811234665.3A CN201811234665A CN109522455A CN 109522455 A CN109522455 A CN 109522455A CN 201811234665 A CN201811234665 A CN 201811234665A CN 109522455 A CN109522455 A CN 109522455A
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point
state
swap
lineage
algorithm
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韦鹏程
黄思行
赵宇
彭亚飞
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Chongqing University of Education
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Abstract

The invention belongs to big diagram data processing technology fields, disclose a kind of overhead method that a large amount of random access of reduction based on half external memory nomography of Swap generate, memory data structure is by one 3 | V | the three-dimensional array of size is constituted;Number of the id as a point in figure;Lineage indicates the attaching information of the point, indicates which switching fabric the point belongs to;Point 1 and the lineage information for putting 4 are all u;State is that a set contains K, N, C, five states of A, P, for describing and defining algorithm.The present invention is on the basis of half external memory Greedy algorithm, the operation based on Scan and state conversion.For the process of one-k-swap, each iteration needs to carry out three-wheel Scan, and the conversion of state in each round can be converted according to state transition rules, and algorithm is persistently iterated, the generation until there will be no swap in current iteration the case where.

Description

The overhead method that a large amount of random access of reduction based on half external memory nomography of Swap generate
Technical field
The invention belongs to big diagram data processing technology field more particularly to a kind of reductions based on half external memory nomography of Swap The overhead method that a large amount of random access generate.
Background technique
Currently, the prior art commonly used in the trade is such that maximum independent set solution is asking substantially for graph theory research field Topic suffers from very important application in fields such as social network analysis, coding theory, wireless sensor network scheduling.Most The solution of big independent sets is also the NP-Hard problem of a famous Combinatorial Optimization.A large amount of research work pairing approximation solves most The problem of big independent sets, is studied, and many approximation algorithms are proposed.Most of these algorithms are theoretically feasible , if but applied in the environment of big diagram data, it is unable to run because the expense of algorithm random access external memory is excessive.This Outside, although some out-of-core algorithms for calculating maximum independent set, cannot also there be theoretical well guarantee because of its randomness.Institute To require to be related to the epoch of diagram data processing in this current many field, design and exploitation efficiently have practical application The maximum independent set derivation algorithm of meaning seems increasingly important.
Maximum independent set problem, one of the basic problem as graph theory field, many traditional derivation algorithms assume that figure Data can be placed directly in memory and handle, but this is for large-scale graph data, impossible is completed (for example, only wrapping Clueweb data containing nodal information occupy disk space 170GB, and general machine can not be directly placed into memory).If straight It connects and these algorithms is realized in a manner of external memory and are applied in the processing of large-scale graph data, then can be visited because of random disk It asks that quantity is too high and causes most of algorithms cannot end of run within reasonable time.So going design big according to conventional thought Diagram data Processing Algorithm will become no longer feasible.In addition, the research of existing some out-of-core algorithms, majority concentrate on theoretic, Seldom it is related to the research of database level.
In conclusion problem of the existing technology is:
(1) derivation algorithm of the prior art assumes that diagram data can be placed directly in memory and handles, but this is for advising greatly It for mould diagram data, can not complete, general machine can not be directly placed into memory.
(2) in these algorithms in the prior art, lead to most of algorithms not because random disk access number is too high It can end of run within reasonable time;Algorithms T-cbmplexity is excessively high, and computer cannot solve in finite time.
Solve the difficulty and meaning of above-mentioned technical problem:: the side for the reduction memory overhead taken when algorithm for design The validity of method, while the expense that a large amount of random access generate is effectively prevented, algorithm is space-efficient.
Summary of the invention
In view of the problems of the existing technology, the present invention provides a kind of reduction based on half external memory nomography of Swap is a large amount of The overhead method that random access generates.
The invention is realized in this way a kind of a large amount of random access generations of reduction based on half external memory nomography of Swap are opened Pin method, the memory data structure for the overhead method that a large amount of random access of reduction based on half external memory nomography of Swap generate By one 3 | V | the three-dimensional array of size is constituted;Three important information that each point is recorded in table, be respectively node number, The state of node and the ownership of node are affiliated " clan ";Number of the id as a point in figure, can be one with unique identification Node;Lineage indicates the attaching information of the point, stores the value of unique independent sets point around the dependent collection point, Indicate which switching fabric the point belongs to;Point 1 and the lineage information for putting 4 are all u;State is that a set contains Five states of K, N, C, A, P, for describing and defining algorithm.
Further, the definition for the overhead method that a large amount of random access of reduction based on half external memory nomography of Swap generate State:
King refers to that the point an of independent sets, Prince refer to this meeting during next wheel scan external memory of algorithm " ascending the throne " becomes the point that state is King, and Aristocrat refers to during algorithm, it is possible to can participate in Swap, it is candidate at For the point of Prince;
Only one blood lineage of the point of each " persons of royal lineage " or ownership, indicate its belong in some switching fabric i.e. its There is only the point of a state K, information is stored in its lineage surrounding, during one-k-Swap algorithm, one State be N dependent collection point by state " N → A → P → K " conversion process gradually becomes an independent sets point;
State C is the point of conflict.
Further, the state for the overhead method that a large amount of random access of reduction based on half external memory nomography of Swap generate Collection: in one-k-Swap algorithm, the set state-set an of state is defined, meets state-set={ K, N, C, A, P }; Neig (u): adjacency list of this in figure is indicated to any one of figure point u, Neig (u);State (u): for any one Point u, state (u) ∈ state-set indicates state of the point u in one-k-swap algorithm;Lineage (u): if a point u, Lineage (u)=w, then having in w ∈ Neig (u) and Neig (u) and only one point w meets state (w)=K;Deadlock (SwapDeadlock): in figure G (V, E), there are two SwapSkeleton, respectively SwapSkeleton (u, p, q) and SwapSkeleton (v, s, t), wherein And access order is p, t, s, q or q, s, p, t.
Another object of the present invention is to provide the reduction based on half external memory nomography of Swap described in a kind of realize largely with The information data processing terminal for the overhead method that machine access generates.
In conclusion advantages of the present invention and good effect are as follows: the present invention is on the basis of half external memory Greedy algorithm, base In the operation that Scan and state are converted.For the process of one-k-swap, each iteration needs to carry out three-wheel Scan, State conversion in each round can be converted according to state transition rules, and algorithm is persistently iterated, until this changes The case where there will be no swap in generation generation.By the size of the number of the obtained maximum independent set of two-k-swap oneself through can be with Close to the 99% of optimal value, the size by the number of the obtained maximum independent set of Greedy is then close to the 96% of optimal value.
Detailed description of the invention
Fig. 1 is opening for reduction a large amount of random access generations provided in an embodiment of the present invention based on half external memory nomography of Swap Sell method flow diagram.
Fig. 2 is the approximation ratio schematic diagram of three kinds of algorithms provided in an embodiment of the present invention.
Fig. 3 is the result and optimum value schematic diagram of two-k-swap provided in an embodiment of the present invention.
Fig. 4 is provided in an embodiment of the present invention based on the corresponding difference P value of Swap-Candidate-Set.
Specific embodiment
In order to make the objectives, technical solutions, and advantages of the present invention clearer, with reference to embodiments, to the present invention It is further elaborated.It should be appreciated that the specific embodiments described herein are merely illustrative of the present invention, it is not used to Limit the present invention.
Application principle of the invention is explained in detail with reference to the accompanying drawing.
As shown in Figure 1, a large amount of random access of the reduction provided in an embodiment of the present invention based on half external memory nomography of Swap produce Raw overhead method the following steps are included:
S101: independent sets neighbor table ISNL is defined, size are as follows: 3 | V | the three-dimensional array of size is constituted, each point of ISNL Three important information be: the ownership or affiliated " clan " of the number id of node, the state state of node and node lineage;
S102:lineage is used to store the value of unique independent sets point around the dependent collection point, indicates the point Which switching fabric belonged to;
S103:state is that a set contains K, N, C, five states of A, P, for describing and defining algorithm;King is Refer to that the point an of independent sets, Prince refer to that this meeting " ascending the throne " during next wheel scan external memory of algorithm becomes state For the point of King (point in independent sets), Aristocrat refers to during algorithm, it is possible to can participate in Swap, it is candidate at For the point of Prince, it is the Primary Actor of algorithm that such point, which is different from the dependent collection point that other states are N,.It is each The point of a " persons of royal lineage " all only one blood lineage or ownership indicate that it belongs in some switching fabric i.e. around it that there is only one The point of a state K, this information are stored in its lineage;
S104: in one-k-Swap step, the point for the dependent collection that a state is N passes through state " N → A → P → The conversion process of K " gradually becomes an independent sets point;
S105: in one-k-Swap algorithm, the set state-set an of state is defined, state-set=is met {K,N,C,A,P}.Neig (u): adjacency list of this in figure is indicated to any one of figure point u, Neig (u).state (u): for any one point u, state (u) ∈ state-set, indicating state of the point u in one-k-swap algorithm;
S106:one-k-Swap, each iteration need to carry out three-wheel Scan, and the state conversion in each round can press It is converted according to state transition rules, algorithm is persistently iterated, the hair until there will be no swap in current iteration the case where It is raw.
Step 5 includes: in a preferred embodiment of the invention
(1) lineage (u): if point u, lineage (u)=w, then having in w ∈ Neig (u) and Neig (u) And only one point w meets state (w)=K;
(2) one-k-Swap structure (one-k-SwapSkeleton): for a figure G (V, E), we define one One-k-Swap structure, one-k-SwapSkeletonCu, v, w), if state (u)=state (v)=A, and state (w)=K, lineage (u)=lineage (v)=w, and there is no side between u and v;
(3) state C is the point of conflict, and in figure G (V, E), there are two SwapSkeleton, respectively SwapSkeleton (u, p, q) and SwapSkeleton (v, s, t), whereinAndAnd access order is p, t, s, q or q, s, p, t.Distinguishingly, when The case where (p, s) ∈ v and when (q, t) ∈ V is also a kind of deadlock.
The expense side that reduction a large amount of random access provided in an embodiment of the present invention based on half external memory nomography of Swap generate Method is One-k-swap algorithm first.Although half out-of-core algorithm can reside in a part of information in memory, calculated with facilitating The progress of method, but its space occupied is C | V |, wherein the value of C can not be too big.For this purpose, the present invention, which devises, to be guaranteed Search speed can reduce the algorithm memory data structure of memory consumption again.It is as shown in the table for data structure, memory data structure by One 3 | V | the three-dimensional array of size is constituted, referred to as independent sets neighbor table, referred to as ISNL.The three of each point are had recorded in table A important information is the number of node, the ownership of the state of node and node or affiliated " clan " respectively.Id is as in figure The number of one point, can be with one node of unique identification.Lineage indicates the attaching information of the point, is used to store the dependent The value of unique independent sets point around collection point, indicates which switching fabric the point belongs to.Point 1 and point 4 Lineage information is all u.State is that a set contains K, N, C, five states of A, P, for describing and defining algorithm.
For the convenience of description, King refers to the point an of independent sets with several special definition of name several states, It is King (in independent sets that Prince, which refers to that this meeting " ascending the throne " during next wheel scan external memory of algorithm becomes state, Point) point, Aristocrat refers to during algorithm, it is possible to can participate in Swap, candidate becomes the point of Prince, in this way Point be different from other states be N dependent collection point, be the Primary Actor of algorithm.The point of each " persons of royal lineage " only has One blood lineage or ownership indicate that it belongs in some switching fabric i.e. around it that there is only the point of a state K, this letters Breath is stored in its lineage.I.e. during one-k-Swap algorithm, the point for the dependent collection that a state is N is logical Crossing state, " N → A → P → K " conversion process gradually becomes an independent sets point.Other than these states, state C is The point of conflict, the setting of this state are " deadlocks " in order to solve the problems, such as to occur during Swap, this is about state Between conversion, will more detailed description in algorithm description part.Before further describing algorithm, first to some bases The definition that this concept and operation is formalized.
State set: in one-k-Swap algorithm, defining the set state-set an of state, meet state-set=K, N,C,A,P}.Neig (u): adjacency list of this in figure is indicated to any one of figure point u, Neig (u).State (u): right In any one point u, state (u) ∈ state-set, state of the point u in one-k-swap algorithm is indicated.Lineage (u): such as One point u, lineage (u)=w of fruit, then having in w ∈ Neig (u) and Neig (u) and only one point w meets state (w) =K.One-k-Swap structure (one-k-SwapSkeleton): for a figure G (V, E), defining an one-k-Swap structure, One-k-SwapSkeletonCu, v, w), if state (u)=state (v)=A, and state (w)=K, lineage (u)=lineage (v)=w, and there is no side between u and v.Deadlock (SwapDeadlock): in figure G (V, E), exist Two SwapSkeleton, respectively SwapSkeleton (u, p, q) and SwapSkeleton (v, s, t), whereinAndAnd access is suitable Sequence is p, t, s, q or q, s, p, t.It distinguishingly, is also a kind of feelings of deadlock when (p, s) ∈ v and (q t) ∈ V Condition.
Application effect of the invention is explained in detail below with reference to emulation.
1, the experimental verification of algorithm
Several algorithms of different that the experiment of this part mainly demonstrates proposition run obtained only on several data sets The comparison of vertical collection size.The one-k-swap and two-k- that table is shown Baseline algorithm and realized based on Baseline algorithm The comparison of the operation result of swap algorithm, one-k-swap and two-k-swap algorithm based on Baseline with introduce before Similar, only external memory diagram data no longer needs to be ranked up according to the degree of node when initial.As can be seen from the table, Effect of the two-k-swap in these three algorithms is best, the effect poor one of one-k-swap ratio two-k-swap A bit, but it is well many than the algorithm of Baseline.Wherein, on the data set as Facebook, one-k-swap and two- The obtained data set of the obtained data set ratio baseline algorithm of k-swap is higher by as many as three times.It is possible thereby to from reality It is verified in effect, the big of independent sets can be gradually increased on the basis of an original maximum independent set by the method for Swap It is small, and an available relatively good result.
Table 1
Similar on table, following table compared Greedy algorithm, and the one-k-swap algorithm based on Greedy algorithm and The comparison of the size for the maximum independent set that two-k-swap algorithm obtains.The available following conclusion from table 1: two-k- The independent sets that swap is obtained are that these three algorithms obtain the independent sets maximum, followed by one-k-swap is obtained, and are finally The independent sets that Greedy is obtained.For Astroph data set, although the effect of Greedy be not it is especially good, After the operation that have passed through Swap, obtained maximum independent set scale still can have a bigger promotion, this also exists The validity of swap operation is demonstrated to a certain extent.
Table 2
Fig. 2 shows the operation of three kinds of algorithms Greedy, one-k-swap and two-k-swap in manually generated data As a result approximation ratio.As shown in the figure, three algorithms all achieve relatively good as a result, wherein one-k-swap and two-k- The result of the approximation ratio of the algorithm of swap is obviously better than Greedy algorithm very much.Fig. 3 compare two-k-swap result and Optimal value as a result, abscissa is the value of each data set, ordinate indicates the number of maximum independent set that algorithm acquires and most The result that the figure of merit obtains.Wherein the calculation method of optimal value is as shown in the algorithm 6 introduced in chapter 4.With manually generated data Collect similar, for most of data set, such as Facebook, for CiteSeerx and UniPort, is obtained by two-k-swap The size of the number of the maximum independent set arrived is own to pass through close to the 99% of optimal value.From this angle alternatively bright algorithm in reality The result of very close optimal value can be obtained in the operation of border.
Experiment presented hereinbefore can be verified substantially, and several half out-of-core algorithms of proposition are ok at most of conditions A relatively good algorithm approximation ratio is obtained, the memory in this section occupying the speed that emphasis carrys out parser operation with it Size.
For several groups of different real data collection, give its correspond to algorithm runing time and one-k-swap and The case where memory overhead of two-k-swap.In terms of the runing time of algorithm, as can be seen from the table, in addition to twine: Except all data sets for, algorithm can terminate in minutes.For example, for comprising close to 6,000 Wan Jiedian For the Facebook data set on 1,500,000,000 sides, the runing time of one-k-swap and two-k-swap were less than 3 minutes, very To for maximum twine: for data set, all algorithms can also be completed within a hour.In memory overhead side Face, the data structure ISNL and Swap-Candidate-Set of algorithm in memory occupied memory during the execution of the algorithm Size.Shown in chart, for all figures, memory overhead for the scale of its diagram data all very It is small, all in the range that half out-of-core algorithm is subjected to (c | V |, wherein c is the constant of a very little).Such as it is occupied on external memory The twitter data set of disk space 9.41GB, the memory overhead of two-k-swap algorithm only have 751.7MB.This can be demonstrate,proved Bright algorithm is space-efficient, also demonstrates having for the method for the reduction memory overhead taken when algorithm for design Effect property.
The reality of the ratio between the size of scale of point of number and Qi Tu for the Swap-Candidate-Set point stored Test data.For the manually generated data of different p values, the ratio be it is relatively stable, it is nearly all attached 0.13 Closely, this also illustrates take in the algorithm Swap-Candidate-Set come recording candidate point collection method be it is feasible, it is this Mechanism does not bring the expense (as shown in Figure 4) of too many memory headroom.
In the above-described embodiments, can come wholly or partly by software, hardware, firmware or any combination thereof real It is existing.When using entirely or partly realizing in the form of a computer program product, the computer program product include one or Multiple computer instructions.When loading on computers or executing the computer program instructions, entirely or partly generate according to Process described in the embodiment of the present invention or function.The computer can be general purpose computer, special purpose computer, computer network Network or other programmable devices.The computer instruction may be stored in a computer readable storage medium, or from one Computer readable storage medium is transmitted to another computer readable storage medium, for example, the computer instruction can be from one A web-site, computer, server or data center pass through wired (such as coaxial cable, optical fiber, Digital Subscriber Line (DSL) Or wireless (such as infrared, wireless, microwave etc.) mode is carried out to another web-site, computer, server or data center Transmission).The computer-readable storage medium can be any usable medium or include one that computer can access The data storage devices such as a or multiple usable mediums integrated server, data center.The usable medium can be magnetic Jie Matter, (for example, floppy disk, hard disk, tape), optical medium (for example, DVD) or semiconductor medium (such as solid state hard disk Solid State Disk (SSD)) etc..
The foregoing is merely illustrative of the preferred embodiments of the present invention, is not intended to limit the invention, all in essence of the invention Made any modifications, equivalent replacements, and improvements etc., should all be included in the protection scope of the present invention within mind and principle.

Claims (6)

1. a kind of overhead method that a large amount of random access of reduction based on half external memory nomography of Swap generate, which is characterized in that institute The memory data structure for the overhead method that a large amount of random access of reduction based on half external memory nomography of Swap generate is stated by one 3 | V | the three-dimensional array of size is constituted;Three important information that each point is recorded in table are the shape of the number of node, node respectively The ownership or affiliated " clan " of state and node;Number of the id as a point in figure, can be with one node of unique identification; Lineage indicates the attaching information of the point, stores the value of unique independent sets point around the dependent collection point, and indicating should Which switching fabric point belongs to;Point 1 and the lineage information for putting 4 are all u;State is that a set contains K, N, C, Five states of A, P, for describing and defining algorithm.
2. the overhead method that a large amount of random access of reduction based on half external memory nomography of Swap generate as described in claim 1, It is characterized in that, the definition shape for the overhead method that a large amount of random access of reduction based on half external memory nomography of Swap generate State:
King refers to that the point an of independent sets, Prince refer to that this meeting during next wheel scan external memory of algorithm " is stepped on Base " becomes the point that state is King, and Aristocrat refers to during algorithm, it is possible to can participate in Swap, candidate becomes The point of Prince;
Only one blood lineage of the point of each " persons of royal lineage " or ownership indicate that it is belonged in some switching fabric i.e. around it There is only the point of a state K, information is stored in its lineage, during one-k-Swap algorithm, a state For N dependent collection point by state " N → A → P → K " conversion process gradually becomes an independent sets point;
State C is the point of conflict.
3. the overhead method that a large amount of random access of reduction based on half external memory nomography of Swap generate as described in claim 1, It is characterized in that, the state set for the overhead method that a large amount of random access of reduction based on half external memory nomography of Swap generate: In one-k-Swap algorithm, the set state-set an of state is defined, meets state-set={ K, N, C, A, P }; Neig (u): adjacency list of this in figure is indicated to any one of figure point u, Neig (u);State (u): for any one A point u, state (u) ∈ state-set indicates state of the point u in one-k-swap algorithm;Lineage (u): if one Point u, lineage (u)=w, then having in w ∈ Neig (u) and Neig (u) and only one point w meets state (w)=K; Deadlock (Swap Deadlock): in figure G (V, E), there are two Swap Skeleton, respectively Swap Skeleton (u, P, q) and Swap Skeleton (v, s, t), wherein And access order is p, t, s, q or q, s, p, t.
4. the overhead method that a large amount of random access of reduction based on half external memory nomography of Swap generate as described in claim 1, It is characterized in that, the overhead method that a large amount of random access of reduction based on half external memory nomography of Swap generate specifically includes:
Step 1 defines independent sets neighbor table ISNL, size are as follows: 3 | V | the three-dimensional array of size is constituted, each point of ISNL Three important information are: the ownership or affiliated " clan " of the number id of node, the state state of node and node lineage;
Step 2, lineage are used to store the value of unique independent sets point around the dependent collection point, indicate that the point is returned Which switching fabric belonged to;
Step 3, state are that a set contains K, N, C, five states of A, P, for describing and defining algorithm;King refers to The point of one independent sets, Prince refer to that this meeting " ascending the throne " during next wheel scan external memory of algorithm as state is The point of King (point in independent sets);Only one blood lineage of the point of each " persons of royal lineage " or ownership, it is a certain to indicate that it is belonged to It is around it in a switching fabric there is only the point of a state K, information is stored in its lineage;
Step 4, in one-k-Swap step, the point for the dependent collection that a state is N passes through " N → A → P → K " of state Conversion process, gradually become an independent sets point;
Step 5 defines the set state-set an of state in one-k-Swap algorithm, meet state-set=K, N,C,A,P};Neig (u): adjacency list of this in figure is indicated to any one of figure point u, Neig (u);state(u): For any one point u, state (u) ∈ state-set, state of the point u in one-k-swap algorithm is indicated;
Step 6, one-k-Swap, each iteration need to carry out three-wheel Scan, and the conversion of state in each round can be according to State transition rules are converted, and algorithm is persistently iterated, the generation until there will be no swap in current iteration the case where.
5. the overhead method that a large amount of random access of reduction based on half external memory nomography of Swap generate as claimed in claim 4, It is characterized in that, the step 5 specifically includes:
(1) lineage (u): if point u, lineage (u)=w, then having in w ∈ Neig (u) and Neig (u) and only There is a point w to meet state (w)=K;
(2) one-k-Swap structure (one-k-Swap Skeleton): for a figure G (V, E), an one-k- is defined Swap structure, one-k-Swap Skeleton Cu, v, w), if state (u)=state (v)=A, and state (w)= K, lineage (u)=lineage (v)=w, and there is no side between u and v;
(3) state C is the point of conflict, and in figure G (V, E), there are two Swap Skeleton, respectively Swap Skeleton (u, p, q) and Swap Skeleton (v, s, t), whereinAndAnd access order is p, t, s, q or q, s, p, t, as (p, s) ∈ The case where v and when (q, t) ∈ V is also a kind of deadlock.
6. a kind of a large amount of random access of reduction realized based on half external memory nomography of Swap described in Claims 1 to 5 any one The information data processing terminal of the overhead method of generation.
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