CN109857676A - The method for reducing random access expense based on Greedy heuristic strategies - Google Patents
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Abstract
The invention belongs to big diagram data processing technology fields；Disclose a kind of method for reducing random access expense based on Greedy heuristic strategies；One state array is set in memory, the status information of node of graph in algorithm is recorded；The state array in memory is initialized by the first row and the second row；The main part of algorithm, when the state of the current node of access is original state, then the point is added in maximum independent set, while being the state of dependent collection by the status modifier of surrounding point；Successively all points in traversing graph, finally obtain this Graph Col oring.Algorithm provided by the invention is all very efficient over time and space, and for most of data therein, the obtained maximum independent set of algorithm of the invention can reach 96% or more of its theoretical upper bound.
Description
Technical field
The invention belongs to big diagram data processing technology fields；More particularly to it is a kind of based on Greedy heuristic strategies reduce with
The method of machine access expense.
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；Current calculator memory has
Big diagram data directly cannot be loaded into memory from external equipment by limit.
(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 one kind reduces random visit based on Greedy heuristic strategies
The method for asking expense.
The invention is realized in this way a method of random access expense, institute are reduced based on Greedy heuristic strategies
Stating the method based on Greedy heuristic strategies reduction random access expense includes:
Step 1: a state array is set in memory, the status information of node of graph in algorithm is recorded；
Step 2: the state array in memory is initialized by the first row and the second row；
Step 3: the main part of algorithm, when the state of the current node of access is original state, then the point
It is added in maximum independent set, while is the state of dependent collection by the status modifier of surrounding point；
Step 4: successively all points in traversing graph finally obtain this Graph Col oring.
Further, the method for the expense that a large amount of random access of reduction of be set forth in Greedy heuristic strategies generate specifically is wrapped
It includes:
Step 1: a state array is set in memory, the status information of node of graph in algorithm is recorded；
Step 2: the state array in memory is initialized；
Step 3: point all in the figure is ranked up all in accordance with the sequence of degree from small to large；
Step 4: select relevant point as the point in independent sets the node of minimum degree since the figure；
Step 5: when the state of the current node of access is original state, then the point can be added to maximum
In independent sets；
Step 6: being the state of dependent collection by the status modifier of surrounding point；
Step 7: successively all points in traversing graph, until not having can a little be added in independent sets；
Step 8: this Graph Col oring is finally obtained.
Further, the main part of the algorithm is the third line to the 12nd row.
Utilization of the invention, which is designed to provide described in a kind of application, reduces random access based on Greedy heuristic strategies
The information data processing terminal of the method for expense.Because ensure that around each independent sets point during selected element
Point is dependent collection point, so the algorithm for solving maximum independent set is correct.
In conclusion advantages of the present invention and good effect are as follows: as shown in Fig. 2, algorithm provided by the invention in the time and
It is all spatially very efficient, and for most of data therein, algorithm of the invention is obtained maximum independent
Collection can reach 96% or more of its theoretical upper bound.
(1) as shown in Fig. 2, in terms of memory overhead, the data structure ISNL and Swap- of algorithm in memory
The size of Candidate-Set occupied memory during the execution of the algorithm.Shown in chart, for all figures,
Its memory overhead is all very small for the scale of its diagram data, all in the range that half out-of-core algorithm is subjected to (cV |,
Wherein c is the constant of a very little).
(2) it as shown in Fig. 2, judging from the experimental results, algorithm design is space-efficient, also demonstrates the present invention and is designing
The validity of the method for the reduction memory overhead taken when algorithm.
(3) as shown in figure 3, being directed to the scale of the number for the point that Swap-Candidate-Set is stored and the point of Qi Tu
The experimental data of the ratio between size.For the manually generated data of different p values, the ratio be it is relatively stable, it is several
All near 0.13, the method that the present invention takes Swap-Candidate-Set to carry out recording candidate point collection in the algorithm is illustrated
Be it is feasible, this mechanism does not bring the expense of too many memory headroom.
Detailed description of the invention
Fig. 1 is the method flow provided in an embodiment of the present invention that random access expense is reduced based on Greedy heuristic strategies
Figure.
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.
Aim to solve the problem that existing technical problem, algorithm provided by the invention be all over time and space it is very efficient,
And for most of data therein, the obtained maximum independent set of algorithm of the invention can reach its theoretical upper bound
96% or more.
Application principle of the invention is described in further detail with reference to the accompanying drawing；
As shown in Figure 1, the side provided in an embodiment of the present invention for reducing random access expense based on Greedy heuristic strategies
Method:
S101: a state array is set in memory, the status information of node of graph in algorithm is recorded；
S102: the state array in memory is initialized by the first row and the second row；
S103: the main part of algorithm, when the state of the current node of access is original state, then the point adds
It is added in maximum independent set, while being the state of dependent collection by the status modifier of surrounding point；
S104: successively all points in traversing graph finally obtain this Graph Col oring.
In step S103, the main part of algorithm provided in an embodiment of the present invention is the 12nd row of the third line value.
The method provided in an embodiment of the present invention for reducing random access expense based on Greedy heuristic strategies specifically includes:
Step 1: a state array is set in memory, the status information of node of graph in algorithm is recorded；
Step 2: the state array in memory is initialized；
Step 3: point all in the figure is ranked up all in accordance with the sequence of degree from small to large；
Step 4: select relevant point as the point in independent sets the node of minimum degree since the figure；
Step 5: when the state of the current node of access is original state, then the point can be added to maximum
In independent sets；
Step 6: being the state of dependent collection by the status modifier of surrounding point；
Step 7: successively all points in traversing graph, until not having can a little be added in independent sets；
Step 8: this Graph Col oring is finally obtained.
It elaborates combined with specific embodiments below to application principle of the invention；
Embodiment 1；
1 basic definition and baseline algorithm
Any one figure G (V, E), V are the set of its point, and E is the set on its side.To the neighbours of its any one point v, v
The degree of Neig (v) ∈ V, v are expressed as the number of the point of its neighbour, is expressed as deg (v).One Graph Col oring
And for meeting for any two the point u, v in IAnd for any one point w ∈ V-I, in I
Always there are a point v, so that (v, w) ∈ E.One Graph Col oring is maximum in the independent sets that can be found in the figure
One independent sets.Oneself of the problem of finding maximum independent set, do not have at present for the problem the problem of being proved to be a NP-hard
There is the method for Efficient Solution.
Half external memory maximum independent set derivation algorithm is defined as follows: figure G (V, E) is calculated on given memory M
The algorithm of maximum independent set I is referred to as half external memory maximum independent set derivation algorithm, and M meets: c | V |≤M≤| G |, wherein c is one
The smaller positive integer constant of a value, such as its value can be 2 or 3 etc..The present invention relates to one and half out-of-core algorithms, but
It still has the property of many out-of-core algorithms, so will also will use many external memory in terms of measuring its performance and expense and calculate
The measurement index of method.For the I/O model of external memory, the access time of disk will be significantly larger than the data access time in memory
With the time of CPU operation, the important bottleneck that all algorithms improve is the expense of I/O, and the number of magnetic disc i/o is also to measure external memory
The important indicator of efficiency of algorithm.In out-of-core algorithm, often uses to two kinds of basic external memory operations, be disk scanning respectively
And external sort.Assuming that the size of disk block is B for system, workable memory headroom is M, the number of external memory storage
It is N according to size, then the complexity of the two basic operations is defined as:
In general, for the nomography of external memory, its common basic unit of I/O complexity is measured are as follows: reading file,
The external memory random access expense of sort file and single indicates to be respectively scan (IVI+IEI), sort (IVI+IEI) and O
(I).Invention proves that I/O expense exists.(V) out-of-core algorithm more than, it is substantially infeasible on the figure more than scale 100M,
So being also a basic setting, that is, the random I/O of the algorithm designed to the performance requirement in terms of the I/O in algorithm design
Expense must be smaller than O (V).Meanwhile on this basis, the CPU overhead in memory is also low as far as possible.
In addition to this, another important criteria for measuring the effect of Algorithms of Maximal Independent Set is the approximation of an algorithm
Than the i.e. size of the obtained maximum independent set of algorithm | I | and its optimal value | Ω | ratio, which can be obtained with measure algorithm
Maximum independent set size and itself and theoretical boundary degree of closeness.It is outer according to the basic definition of maximum independent set problem and half
The thought of algorithm is deposited, can intuitively expect a kind of baseline algorithm the simplest, referred to as SemiExternalBaseline
Algorithm.The basic thought of algorithm is the information feature using adjacency list, carries out a Scan to the file on external memory, in memory
Safeguard the access information of node, what Scan was obtained is then added in maximum independent set without the point that accessed, all neighbours
Occupy the point concentrated labeled as dependent.Algorithm 2 is the pseudocode of the algorithm, which only needs to carry out the file of external memory primary
The memory headroom of Scan, occupancy is | V |.The algorithm is an ordinary algorithm, and algorithm has stronger randomness, without foot
Enough theoretical guarantees, are also being good or bad because of the difference of data set in actual effect, have with the sequence of external memory interior joint very big
Relationship.
2 half out-of-core algorithms based on GREEDY
Theoretically there is extraordinary result using the algorithm that the memory of Greedy rule design solves maximum independent set.
By the inspiration of this algorithm, the heuristic rule that Greedy is utilized on external memory is attempted, to design new algorithm, to obtain more
Good Algorithms of Maximal Independent Set.
Due to constantly carrying out the random access of dynamic order and other nodes to the node of diagram data on external memory, will cause
A large amount of I/O accesses expense, and for larger diagram data, this random I/O accesses expense, algorithm can be allowed not do
Method terminates at the appointed time.So with the sequence of a kind of " static state ", instead of " dynamic " sequence, to complete new Greedy
Algorithm.
Half external memory solves the greedy algorithm of Graph Col oring problem, and the main thought of algorithm will be all in the figure
Point is ranked up all in accordance with the sequence of degree from small to large, then successively selects relevant point as the point in independent sets, until not having
Until being a little added in independent sets.The present invention is provided with a state array in memory, schemes for recording in algorithm
The status information of node.
The first row and the second row are initialized to the state array in memory；
The 12nd row of the third line value is the main part of algorithm, when the state of the current node of access is original state
When, then the point can be added in maximum independent set, while be the shape of dependent collection by the status modifier of surrounding point
State.
Successively all points in traversing graph, finally obtain this Graph Col oring.
Because ensure that the point around each independent sets point is dependent collection point during selected element, so
The algorithm that the present invention solves maximum independent set is correct.
It is described in further detail below with reference to application principle of the specific experiment to invention；
1 data set and experimental situation
All algorithms realize that translation and compiling environment is Visual C++2010 using C++, experiment fortune of the invention
Capable machine is configured that Core i5 4.0GHz CPU, 4GB RAM and Seagate ST3500413AS hard disk (500GB/
7200 revs/min), system is 7 operating system of Windows.Data set is as follows:
Table 1: the function of data set and data set
The experimental verification of 2 algorithms
Following table compared Greedy algorithm, and one-k-swap algorithm and two-k-swap algorithm based on Greedy algorithm
The comparison of the size of obtained maximum independent set.The present invention can obtain following conclusions from table: two-k-swap is obtained
Independent sets be these three algorithms obtain the independent sets maximum, followed by one-k-swap is obtained, be finally that Greedy is obtained
The independent sets arrived.Contrast table, it is found that for most of data set, Greedy algorithm obtains maximum independent set
The number of number maximum independent set obtained than Baseline is larger.One data set of sole exception is Astroph number
According to collection, reason for that is that the distribution of the degree of Astroph data centralized node is relatively uniform, is unsatisfactory for the random artwork of power-law distribution
To the requirement of the distribution of point in type, so being even ranked up to the degree of its node, the effect of its algorithm can not be improved.It is right
For Astroph data set, although the effect of Greedy be not it is especially good, after the operation that have passed through Swap,
Its obtained maximum independent set scale still can have a bigger promotion, this also demonstrates swap behaviour to a certain extent
The validity of work.
Table 3: the influence situation of 1-k-swap and 2-k-swap based on greedy algorithm and greedy algorithm
By parser approximation ratio, i.e. the property of carrying out parser of ratio between the result and optimal value of the acquisition of algorithm
Energy.
As shown in Fig. 2, the operation of three kinds of algorithms Greedy, one-k-swap and two-k-swap in manually generated data
As a result approximation ratio.Three algorithms all achieve relatively good as a result, the wherein algorithm of one-k-swap and two-k-swap
The result of approximation ratio is obviously better than Greedy algorithm very much.In addition, the approximation ratio of algorithm is all with the increase of data set p value
Increasing.The reason of generating this phenomenon is, with the increase of p value, it is meant that the quantity on the side that the artificial data of generation is concentrated
It is fewer, so algorithm can obtain relatively good result.
As shown in figure 3, compare two-k-swap result and optimal value as a result, abscissa be each data set value,
Ordinate indicates the result that the number for the maximum independent set that algorithm acquires and optimal value obtain.With manually generated data set class
Seemingly, it for most of data set, such as Facebook, for CiteSeerx and UniPort, is obtained by two-k-swap
The size of the number of maximum independent set is own to pass through close to the 99% of optimal value.From this angle alternatively bright algorithm in practical fortune
The result of very close optimal value can be obtained in the trade.
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 of the invention is space-efficient, also demonstrates the reduction memory that the present invention is taken when algorithm for design and opens
The validity of the method for pin.
As shown in figure 4, the scale of the point of number and Qi Tu for the Swap-Candidate-Set point stored is big
The ratio between small experimental data.For the manually generated data of different p values, the ratio be it is relatively stable, almost
All near 0.13, this also illustrates the sides of the invention for taking Swap-Candidate-Set to carry out recording candidate point collection in the algorithm
Method be it is feasible, this mechanism does not bring the expense of too many memory headroom.
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 (4)
1. a kind of method for reducing random access expense based on Greedy heuristic strategies, which is characterized in that be set forth in Greedy
The method for the expense that a large amount of random access of reduction of heuristic strategies generate includes:
Step 1: a state array is set in memory, the status information of node of graph in algorithm is recorded；
Step 2: the state array in memory is initialized by the first row and the second row；
Step 3: the main part of algorithm, when the state of the current node of access is original state, then the point adds
It is the state of dependent collection in maximum independent set, while by the status modifier of surrounding point；
Step 4: successively all points in traversing graph finally obtain this Graph Col oring.
2. the method for reducing random access expense based on Greedy heuristic strategies as described in claim 1, which is characterized in that
The method for the expense that a large amount of random access of reduction of be set forth in Greedy heuristic strategies generate specifically includes:
Step 1: a state array is set in memory, the status information of node of graph in algorithm is recorded；
Step 2: the state array in memory is initialized；
Step 3: point all in the figure is ranked up all in accordance with the sequence of degree from small to large；
Step 4: select relevant point as the point in independent sets the node of minimum degree since the figure；
Step 5: when the state of the current node of access is original state, then the point can be added to maximum independent
In collection；
Step 6: being the state of dependent collection by the status modifier of surrounding point；
Step 7: successively all points in traversing graph, until not having can a little be added in independent sets；
Step 8: this Graph Col oring is finally obtained.
3. the method for reducing random access expense based on Greedy heuristic strategies as described in claim 1, which is characterized in that
The main part of the algorithm is the third line to the 12nd row.
4. a kind of reduce random access expense based on Greedy heuristic strategies using described in claims 1 to 3 any one
The information data processing terminal of method.
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Citations (3)
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| CN104065509A (en) * | 2014-07-24 | 2014-09-24 | 大连理工大学 | SDN multi-controller deployment method for reducing management load overhead |
| CN105912404A (en) * | 2016-04-27 | 2016-08-31 | 华中科技大学 | Method for searching strongly connected component in large-scale graph data on the basis of disk |
| CN107992572A (en) * | 2017-11-30 | 2018-05-04 | 天津大学 | A kind of distributed graph coloring algorithm based on Pregel |
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2018
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| CN104065509A (en) * | 2014-07-24 | 2014-09-24 | 大连理工大学 | SDN multi-controller deployment method for reducing management load overhead |
| CN105912404A (en) * | 2016-04-27 | 2016-08-31 | 华中科技大学 | Method for searching strongly connected component in large-scale graph data on the basis of disk |
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