CN103491128A - Optimal placement method for popular resource duplicates in peer-to-peer network - Google Patents

Abstract

The invention relates to an optimal placement method for popular resource duplicates in a peer-to-peer network. According to the method, mathematical abstraction is performed on the connectedness between nodes of storage duplicates, the load balance of nodes of placement nodes and other technological difficulties in the peer-to-peer network, and a resource optimal placement model is provided from the point of view of mathematics, so that the searching success rates of popular files in the peer-to-peer network are improved; meanwhile the node overheads for storing the popular files are reduced, so that the total overheads of the whole network are reduced, and the network has better expansibility.

Description

The optimization laying method of popular Resource Replica in a kind of peer-to-peer network

Technical field

The present invention relates to network communication field, particularly the peer-to-peer network search is optimized and resource placement optimization problem.

Background technology

Peer-to-peer network is the key concept of next generation network, different from traditional central server and client mode.In peer-to-peer network, each node both obtained from all the other nodes the resource of oneself wanting, and also to remaining node, provided own shared resource.In the realization of peer-to-peer network, owing to there not being central server, how locating fast various resources and service is a key technology.

The current research about fast search in peer-to-peer network has been divided into structure peer-to-peer network and non-structure peer-to-peer network by peer-to-peer network.The non-structure peer-to-peer network compares to the structure peer-to-peer network that uses distributed hashtable (Distributed Hash Table), and search efficiency is on the low side, but himself maintenance costs significantly reduces, and has good autgmentability, be convenient on a large scale in networking.

In the non-structure peer-to-peer network, the search of information is divided into blind search and guidance quality search.Blind search be take and flooded (Flooding) search for basis, and it is indiscriminate that node will be searched for information, or several neighbor nodes of random selection are forwarded, and search for and have blindness; The common technology of guidance quality search is according to some tutorial messages, inquiry request to be forwarded to and to search on the node had higher success rate.

The information that instructs inquiry request to forward in guidance quality search can be the search history of node or content similitude etc., therefore its forward node is often followed through and is ask node and have some identical character, such as having similar storage content, or similar line duration etc.The guidance quality search is larger than the success rate of blind search to a certain extent, has reduced the information redundancy in the network simultaneously and has increased.But after after a while, because the content of its maintenance of part of nodes in network is more, and service ability good (for example, the small server in some areas), make its common forward node that becomes all mid-side nodes gradually.So just formed the overheated node of some in the peer-to-peer network or be referred to as super node, they are bearing processing and the forwarding of searching for greatly information in network.

In peer-to-peer network, the existence of overheated node is a hidden danger.Overheated node, due to processing and the forwarding of carrying too much search information, likely there will be the situation of overload, causes subregion in network the situations such as information obstruction to occur.Thereby the leaf node of enjoying service by this super node may suffer from the situation that search response postpones.Therefore need to reduce as much as possible the expense of super node, can be better leaf node service on every side.

In order to solve the excessive node superheating phenomenon caused of popular resource access amount, current common technology is the copy of the popular resource of reasonable buffer memory, thereby reduces the expense of overheated node.The basic principle of this technology is that the copy of popular resource is stored in network on part of nodes, when having identical search information to be forwarded to these nodes, node finds that resource of this search information request is identical with the copy of self buffer memory, direct and query node connects and carry out the transmission of copy.This technology can effectively reduce the expense of overheated node and improve the response time (Fig. 2) of service.

Existing copy placement technique has had many achievements in research.The frequency that is queried according to resource had copies accordingly to resource, by more node, meets inquiry to reduce the search communication overhead, has obtained good effect.

A key issue of copy caching technology is the validity that will guarantee that copy is placed, and the node of cached copies will have with corresponding super node certain behavior similarity feature, thereby can effectively reduce the expense of super node.Current common technology is that the validity that cache-time is guaranteed copy is set.

In addition, current technology exists the phenomenon that the copy redundancy is placed in the process realized.In the small-scale local area network (LAN), because node is all relative less with resource, redundancy is placed and can not produced a very large impact node.And, in networking on a large scale, in especially dense network, node may cause collapse due to the too much storage demand of carrying, affected the extensibility of network.

Summary of the invention

The problem that technology of the present invention solves: overcome the deficiencies in the prior art, the optimization laying method of popular Resource Replica in a kind of peer-to-peer network is provided, the method can effectively reduce the super node expense of the popular resource of storage in network, improves the extensibility of Searching algorithm.

Technical solution of the present invention: the optimization laying method of popular Resource Replica in a kind of peer-to-peer network, performing step is as shown in Figure 1, specific as follows:

A. when each cycle of operation of peer-to-peer network starts, self the accessed number of times in the upper one-period of each node statistics in network;

B. each node determines oneself to be leaf node or super node according to access times, and the node definition that access times surpass setting threshold is popular node, also is referred to as super node, and the node that access times do not reach threshold value is called leaf node; All nodes send an information that shows own identity to the node around it, thereby in network, each node is known super node and leaf node on every side;

C. identity information described in the step B that super node receives according to oneself, count the leaf node in own routing table, and calculate described these leaf nodes and factum similitude; Behavioral similarity between described leaf node and super node refers to the proportion of interior leaf node of last cycle and the common line duration of super node.In addition, interior self resource access number of times of a upper cycle of super node statistics, be popular resource by access times higher than the resources definition of setting threshold;

D. described leaf node can provide self memory capacity and routing table information send to super node.Described super node, according to the information of the leaf node received, counts the degree of communication between these leaf nodes;

E. super node is according to the behavioral similarity of self and the leaf described in step C, and the degree of communication information between the leaf node described in D and the storage capacity information of leaf node, set up integer programming model, the optimization aim of model is that super node is placed the least possible popular duplicate of the document, reduces the super node expense simultaneously.Described integer programming model is respectively:

Reduce the integer Optimized model of super node expense:

$\min \underset{n=1}{\overset{k}{\mathrm{\Σ}}}\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{X}_{\mathrm{nij}}---\left(1\right)$

$\begin{array}{cccc}s.t& \underset{j=1}{\overset{m}{\mathrm{\Σ}}}{P}_{\mathrm{ij}}\·X_{\mathrm{nij}}\≥\mathrm{\λ}& (n=\mathrm{1,2},\·\·\·k)& (\mathrm{\λ}\≥1)\end{array}---\left(2\right)$

$\begin{array}{cc}\underset{n=1}{\overset{k}{\mathrm{\Σ}}}{X}_{\mathrm{nij}}\·C_n\≤D_j& (j=\mathrm{1,2},\·\·\·m)\end{array}---\left(4\right)$

X _nij＝0,1 （5）

Wherein: X _nijsuper node SN is described _iby popular resource f _ncopy be stored in leaf node N _jupper this event, X _nij=1 is illustrated in N _jstore this copy, otherwise X _nijthe number that=0, m is leaf node, k is copy number to be placed;

P in the constraints of model (2) _ijmean super node SN _iby popular resource f _ncopy be stored in leaf node N _jprobability, P _ijcan mean with behavioral similarity, λ is a given threshold value;

Ω in the constraints of model (3) _nmean the set of leaf node, T _p, T _qthat mean is leaf node N _p, N _qrouting table in node set, what mean is to have common neighbor node in these leaf node routing tables, and now same file only need to be placed at the most a copy on these leaf nodes, thereby reduces the resource placement expense of network;

The constraints of model (4) means that the total capacity of node stored copies can not surpass the storage space volume that node self provides, wherein C _nthe capacity that means resource n, D _jmean the spatial cache capacity that node j can provide;

F. integer programming model described in solution procedure E, draw the leaf node set of placing Resource Replica;

G. super node is cached to the copy of the popular resource described in step C on leaf node corresponding in the optimal solution of step F gained.

Time period unit of all index futures in described steps A, be one week or one month etc., and its concrete time span depends on the load of network and the popular time of resource, the situations such as renewal frequency.

In described step C, the computing formula of behavior similarity is:

$\mathrm{Sim}(N_i,N_j)=\frac{T_i\∩T_j}{T}$

Wherein, use N _i, N _jmean any two nodes in network.Sim (N _i, N _j) expression N _i, N _jbetween the behavior similarity.T means the duration of one-period.T _i, T _jmean respectively node N _i, N _jline duration in the T duration, T _i∩ T _jmean N _i, N _jcommon online hours in the T duration.In concrete enforcement, each node sends a message to the node in its routing table at every turn when entering network and deviated from network, thereby the node in routing table can count the online hours of this node.

In described step D, super node is first added up the degree of communication between leaf node in its routing table at every turn before starting to place copy.Optional two leaf node N wherein _i, N _jafter they send to super node by self routing table information, super node is compared the node ID in the leaf node routing table, jointly can reach node if exist except super node, only on a leaf node therein, place a copy of same file at the most, thereby the resource that reduces network is placed expense.

In described step F, adopt greedy algorithm to go to ask integer programming model, concrete steps are:

Step 1: choose arbitrarily the super node of a popular resource of storage in network, be expressed as SN _i.At first calculate SN _ileaf node N in routing table ₁, N ₂..., N _nwith SN _ithe behavior similarity, the sum that wherein n is the leaf node in routing table, obtain similarity set P=(p ₁, p ₂... p _n), each component p wherein _i(i=1,2 ... n) mean SN _iwith leaf node N _icommon online hours proportion in one-period.If super node SN _iin routing table, a leaf node does not have yet,

algorithm stops; Otherwise descending sort obtains P '=(p to P ₁', p ₂' ... p _n').If optimal solution set S is empty set,

go to step 2;

Step 2: if the leaf node number that in optimal solution, super node connects surpasses the setting threshold λ in constraints (2), algorithm stops, output optimal solution set S; Otherwise, go to step 3;

Step 3: suppose that in current P ', first component is p _k' (when calculating for the first time, k=1).Find p _k' corresponding leaf node N _k, and upgrade P ', update method is by p _k' from P ', remove, if having leaf node and N in optimal solution set S _kbetween common neighbor node number is arranged, have N _j∈ S, make

cast out N _k, and repeated execution of steps 3; Otherwise go to step 4;

Step 4: use N _jmean the leaf node in current S set.Now need to calculate N _kwhether surpass setting threshold λ with the desired number of leaf node in S,

p wherein _ijadopt the similarity value of calculating in step 1, subscript i, j is corresponding super node SN _iwith leaf node N _jsubscript.If surpass threshold value, by N _kadd the optimal solution set, now upgrade S=S ∪ N _k, obtain placing the leaf node S set of copy and stopping algorithm output S; Otherwise by N _kadd the optimal solution set, S=S ∪ N _k, go to step 3.

From big to small examine or check each leaf node according to internodal behavior similarity in the present invention when solving the target function of model, the reason of operation is because leaf node and the common line duration of super node that at first similarity is high are longer like this, it is corresponding Resource Supply service that copy can have the longer time after placing, thus the expense of super node in having reduced during this period of time; Secondly, placing under this target of minimum number of copies this selection scheme can satisfy condition as early as possible (2) under the constraint of condition (3).

When having several constraintss (3), super node has met constraints (2) after having placed copy on may the leaf node high in several similarities.Now, remaining leaf node can be placed copy.This is because, after condition (2) establishment, the copy of this resource can meet the demand of most of nodes, so place, finishes;

This model exists in theory without the situation of separating: when there being certain leaf node N _ivery high with the super node similarity, and also very high with the degree of communication of several leaf nodes on every side.Model is according to greedy algorithm after preferentially placing the leaf node that similarity is higher, and according to constraints (3), remaining leaf node does not need to place wave file again, thereby because the situation that finally can't reach restrictive condition (2) causes model without solution.But in real network, if there is this situation in a leaf node,, under the principle of guidance quality search, node is on every side found by the search success rate after this node forwarding inquiries information higher gradually, can preferentially select this node when search forwards, therefore will cause N _ithe information processing of carrying increases, and becomes an overheated node.N _iitself just is not present in the leaf node set of model solution.

The present invention's advantage compared with prior art is: the actual conditions that the present invention is based on node in peer-to-peer network, by the definition of introducing behavioral similarity solved node dynamically on the factor such as roll off the production line, make the placement of copy have more practical function compared to the placement result under static network.Simultaneously, by the statistics of the degree of communication to leaf node, make in network the distribution of copy more balanced.Finally, all investigation factors have been set up to a model that resource optimization is placed by mathematical abstractions, and provided method for solving, reduced thus the expense of the node of storage flow style of writing part in the peer-to-peer network.

The accompanying drawing explanation

Fig. 1 is popular Resource Replica laying method flow chart in peer-to-peer network of the present invention;

The schematic diagram that Fig. 2 is the copy caching technology;

Fig. 3 is the present invention's enforcement illustration that copy is placed in network.

Embodiment

Peer-to-peer network is to consist of one group of terminal equipment of linking in network, these terminal equipments can be desktop computer, the portable notebook computer of general family expenses, the small server of better performances, or the server of a small area, they form each node in this peer-to-peer network jointly.Each equipment has the function of data route, puts down in writing the visit capacity of own resource simultaneously, the information such as self line duration.Each equipment peripherad node when the network operation sends announcement information, comprise the node identity information, on roll off the production line temporal information and copy place solicited message etc.The leaf node that each super node is placed according to these Information Selection copies.

Place the response time that can improve resource searching in peer-to-peer network by copy, and reduced the expense of super node.As shown in Figure 2, at first PC2 sends the search of a resource, and after 2 jumpings, in Fig. 2, rightmost server place searches the resource of request.But, now because server can't respond the download request of PC2 to resource in time in superheat state, the node PC1 that instructs PC2 to forward this Resource Replica of buffer memory to goes to download.Therefore, by realize the caching technology of copy at the PC1 place, effectively promoted the resource downloading response time of PC2 and alleviated the processing expenditure of server.

In peer-to-peer network, node has dynamic, so the copy laying method described in Fig. 2, in peer-to-peer network, the PC1 node off-line may occur, thereby cause the copy of placing, can't be the situation of PC2 service.So whether we consider between node in invention simultaneously online, and how balanced placement copy is all node services.

For making the present invention easier to understand, the flow chart in conjunction with an example (Fig. 3) to Fig. 1 of the present invention is further elaborated, but this example does not form any limitation of the invention.

Fig. 3 is nine of the parts node diagram of peer-to-peer network, and in figure, nine nodes were added up as following table in the visit capacity in a upper cycle:

Table 1: a cycle access number of times statistics on node

Node1

Node2

Node3

Node4

Node5

Node6

Node7

Node8

Node9

621

36

89

57

90

87

61

48

153

According to the information in table, node1 becomes a super node SN ₁.All the other nodes become 8 leaf node (N in the defeated scope of one jump set ₁, N ₂..., N ₈).SN ₁when one-period starts, receive the line duration of all the other 8 nodes and calculate itself and N according to calculating formula of similarity in described step C ₁, N ₂..., N ₈behavioral similarity.Its behavioral similarity is as shown in table 2 after calculating: (cycle is got a week),

Table 2: leaf node N ₁, N ₂..., N ₈with super node SN ₁behavioral similarity

	N 1	N 2	N 3	N 4	N 5	N 6	N 7	N 8
									SIM	25%	75%	77%	29%	42%	54%	61%	84%

In addition, SN ₁receive leaf node N ₁, N ₂..., N ₈the routing table information reported, calculate (N according to step D ₁, N ₂..., N ₈) between degree of communication.As shown in table 3.

Table 3: leaf node N ₁, N ₂..., N ₈between degree of communication

	N 1	N 2	N 3	N 4	N 5	N 6	N 7	N 8
									N 1	×	0	0	0	0	0	0	0
N 2	0	×	0	0	1	0	0	0
									N 3	0	0	×0	0	0	0	1	0
N 4	0	0	0	×	0	0	0	1
									N 5	0	1	0	0	×	0	0	0
N 6	0	0	0	0	0	×	0	0
									N 7	0	0	1	0	0	0	×	0
N 8	0	0	0	1	0	0	0	×

In table, element 0 means not have public-neighbor between node, and 1 means to exist public-neighbor., there is identical neighbor node in node 2 and node 5 between node 3 and node 7 and node 4 and node 8 as shown in Table 2.

The target that this example solves is to place the expense that less copy resource effectively alleviates super node.The constraints that can list Optimized model according to table 3 is:

X ₁₂+X ₁₅≤1;

X ₁₃+X ₁₇≤1;

X ₁₄+X ₁₈≤1；

All the other parameters that model needs are:

Table 4: leaf node N ₁, N ₂..., N ₈spatial cache be: (unit: MB)

N 1	N 2	N 3	N 4	N 5	N 6	N 7	N 8
								2046	2198	3487	5578	1863	3824	793	5042

The copy size that popular resource is set in example of the present invention is 1030MB.This resource need at least be placed three above copies in the neighbor node of a jumping just can effectively alleviate processing and the transport overhead of super node, and concrete model is as follows:

$\min \underset{j=1}{\overset{m}{\mathrm{\Σ}}}{X}_{\mathrm{nij}}$

$\begin{array}{cc}s.t.& \underset{j=1}{\overset{m}{\mathrm{\Σ}}}{P}_{\mathrm{ij}}\·X_{\mathrm{nij}}\≥3\end{array}$

X ₁₂+X ₁₅≤1;

X ₁₃+X ₁₇≤1;

X ₁₄+X ₁₈≤1；

X _n11·1030≤2046；

X _n12·1030≤2198；

X _n13·1030≤3487；

X _n14·1030≤5578；

X _n15·1030≤1863；

X _n16·1030≤3824；

X _n17·1030≤793；

X _n18·1030≤5042

X _nij＝0,1

Because the scale of this problem is less, can take the greedy algorithm of similar knapsack problem to be solved, at first according to N ₁, N ₂..., N ₈with SN ₁similarity according to descending sort, be:

(N ₈,N ₃,N ₂,N ₇,N ₆,N ₅,N ₄,N ₁)

The highest N in similarity ₈upper placement copy, N as shown in Table 3 ₈spatial cache can place copy, so copy successfully is cached to N ₈.Then be placed on successively N ₃, N ₂upper, now due to restrictive condition X ₁₃+ X ₁₇≤ 1, N ₇can not need to place copy.Then consider at N ₆upper placement copy, N ₆spatial cache can successful cached copies and with node N before ₈, N ₃, N ₂do not have common neighbor node, so copy successfully is cached in N ₆.Same analysis is known, N ₅, N ₄can't cached copies, N ₁can cached copies.Now:

$\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{P}_{\mathrm{ij}}\·X_{\mathrm{nij}}=84\%\·1+77\%\·1+75\%\·1+54\%\·1+25\%\·1\≥3$

Met the condition of model, optimal solution is X=(N ₈, N ₃, N ₂, N ₆, N ₁).SN ₁according to optimal solution, copy is placed on corresponding leaf node, on the leaf node around by this method the copy of a popular resource successfully being cached to, thereby has alleviated the expense of super node.

Non-elaborated part of the present invention belongs to techniques well known.

The above is embodiments of the present invention; certainly can not limit with this interest field of the present invention; should be understood that; for those skilled in the art; under the premise without departing from the principles of the invention, can also make some improvement and change, for the setting of cycle duration; can get different values according to the popularity of concrete resources in network and the actual conditions such as performance of node, these improvement and change also are considered as protection scope of the present invention.

Claims (5)

1. the optimization laying method of popular Resource Replica in a peer-to-peer network is characterized in that performing step is as follows:

A. when each cycle of operation of peer-to-peer network starts, self the accessed number of times in the upper one-period of each node statistics in peer-to-peer network;

B. each node determines oneself to be leaf node or super node according to access times, and the node definition that access times surpass setting threshold is popular node, also is referred to as super node, and the node that access times do not reach threshold value is called leaf node; All nodes send an information that shows own identity to the node around it, thereby in peer-to-peer network, each node is known own super node and leaf node information on every side;

C. identity information described in the step B that super node receives according to oneself, count the leaf node in own routing table, and calculate described these leaf nodes and factum similitude; Behavioral similarity between described leaf node and super node refers to the proportion of interior leaf node of last cycle and the common line duration of super node; In addition, interior self resource access number of times of a upper cycle of super node statistics, be popular resource by access times higher than the resources definition of setting threshold;

D. described leaf node provides self memory capacity and routing table information send to super node, and described super node, according to the information of the leaf node received, counts the degree of communication between these leaf nodes;

E. super node according to described in step C and leaf between behavioral similarity, and the degree of communication information between the leaf node described in D and the storage capacity information of leaf node, set up integer programming model, the optimization aim of model is that super node is placed the least possible popular duplicate of the document, reduces the super node expense simultaneously;

The integer Optimized model that reduces the super node expense is:

$\min \underset{n=1}{\overset{k}{\mathrm{\Σ}}}\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{X}_{\mathrm{nij}}---\left(1\right)$

$\begin{array}{cccc}s.t& \underset{j=1}{\overset{m}{\mathrm{\Σ}}}{P}_{\mathrm{ij}}\·X_{\mathrm{nij}}\≥\mathrm{\λ}& n=\mathrm{1,2},\·\·\·k& \mathrm{\λ}\≥1\end{array}---\left(2\right)$

$\begin{array}{cc}\underset{n=1}{\overset{k}{\mathrm{\Σ}}}{X}_{\mathrm{nij}}\·C_n\≤D_j& j=\mathrm{1,2},\·\·\·m\end{array}---\left(4\right)$

X _nij＝0,1 （5）

X in the target function of model (1) _nijsuper node SN is described _iby popular resource f _ncopy be stored in leaf node N _jupper this event, X _nij=1 means N _jstore this copy, otherwise X _nijthe number that=0, m is leaf node, k is copy number to be placed;

P in the constraints of model (2) _ijmean super node SN _iby popular resource f _ncopy be stored in leaf node N _jprobability, P _ijwith behavioral similarity, mean, λ is a given threshold value;

Ω in the constraints of model (3) _nmean the set of leaf node, T _p, T _qthat mean is leaf node N _p, N _qrouting table in node set,

mean to have common neighbor node in these leaf node routing tables, now same file only need to be placed at the most a copy on these leaf nodes, thereby reduces the resource placement expense of network;

The constraints of model (4) means that the total capacity of node stored copies can not surpass the storage space volume that node self provides, wherein C _nthe capacity that means resource n, D _jmean the spatial cache capacity that node j can provide;

F. integer programming model described in solution procedure E, draw the leaf node set of placing Resource Replica;

G. super node is cached to the copy of the popular resource described in step C on leaf node corresponding in the optimal solution of step F gained.

2. the optimization laying method of popular Resource Replica in a kind of peer-to-peer network according to claim 1, it is characterized in that: time period unit of all index futures in described steps A, it is one week or one month, concrete time span depends on the load of network and the popular time of resource, renewal frequency situation.

3. the optimization laying method of popular Resource Replica in a kind of peer-to-peer network according to claim 1, it is characterized in that: in described step C, the computing formula of behavior similarity is:

$\mathrm{Sim}(N_i,N_j)=\frac{T_i\∩T_j}{T}$

Wherein, use N _i, N _jmean any two nodes in network; Sim (N _i, N _j) expression N _i, N _jbetween the behavior similarity; T means the duration of one-period.T _i, T _jmean respectively node N _i, N _jline duration in the T duration, T _i∩ T _jmean N _i, N _jcommon online hours in the T duration; When concrete enforcement, each node sends a message to the node in its routing table at every turn when entering network and deviated from network, thereby the node in routing table can count the online hours of this node.

4. the optimization laying method of popular Resource Replica in a kind of peer-to-peer network according to claim 1 is characterized in that: in described step D super node first add up routing table before starting to place copy at every turn in degree of communication between leaf node.Concrete grammar is: optional two leaf node N wherein _i, N _jafter they send to super node by self routing table information, super node is compared the node ID in the leaf node routing table, jointly can reach node if exist except super node, only on a leaf node therein, place a copy of same file at the most, thereby the resource that reduces network is placed expense.

5. the optimization laying method of popular Resource Replica in a kind of peer-to-peer network according to claim 1 is characterized in that: in described step F, adopt greedy algorithm to go to solve integer programming model, concrete steps are:

Step 5.1: choose arbitrarily the super node of a popular resource of storage in network, be expressed as SN _i; At first calculate SN _ileaf node N in routing table ₁, N ₂..., N _nwith SN _ithe behavior similarity, the sum that wherein n is the leaf node in routing table, obtain similarity set P=(p ₁, p ₂... p _n), each component p wherein _i(i=1,2 ... n) mean SN _iwith leaf node N _icommon online hours proportion in one-period; If super node SN _iin routing table, a leaf node does not have yet,

algorithm stops; Otherwise descending sort obtains P '=(p to P ₁', p ₂' ... p _n'), establishing optimal solution set S is empty set,

go to step 5.2;

Step 5.2: if the leaf node number that in optimal solution, super node connects surpasses the setting threshold λ in constraints (2), algorithm stops, output optimal solution set S; Otherwise, go to step 5.3;

Step 5.3: suppose that in current P ', first component is p _k', find p _k' corresponding leaf node N _k, and upgrade P ', update method is by p _k' from P ', remove, if having leaf node and N in optimal solution set S _kbetween common neighbor node number is arranged, have N _j∈ S, make

cast out N _k, and repeated execution of steps 5.3; Otherwise go to step 5.4;

Step 5.4: use N _jmean the leaf node in current S set.Now need to calculate N _kwhether surpass setting threshold λ with the desired number of leaf node in S,

p wherein _ijadopt the similarity value of calculating in step 5.1, subscript i, j is corresponding super node SN _iwith leaf node N _jsubscript; If surpass threshold value, by N _kadd the optimal solution set, now upgrade S=S ∪ N _k, obtain placing the leaf node S set of copy and stopping algorithm output S; Otherwise by N _kadd the optimal solution set, S=S ∪ N _k, go to step 5.3.

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