CN109388772A - A kind of taboo search method that time-based Large Scale Graphs equilibrium k is divided - Google Patents
A kind of taboo search method that time-based Large Scale Graphs equilibrium k is divided Download PDFInfo
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- CN109388772A CN109388772A CN201811024190.5A CN201811024190A CN109388772A CN 109388772 A CN109388772 A CN 109388772A CN 201811024190 A CN201811024190 A CN 201811024190A CN 109388772 A CN109388772 A CN 109388772A
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Abstract
The present invention discloses a kind of taboo search method that time-based Large Scale Graphs equilibrium k is divided comprising the steps of: 1, calculate and count each partition running time；2, partition running time T is calculatedDiIllustrate that the partition running time is within the acceptable range if difference is less than threshold value with the difference of average operating time, if difference is greater than threshold value, then illustrate to need to shift vertex, to reduce local computing time or call duration time, to reduce the partition running time；3, the financial value of vertex v is calculated, the maximum sub-district of financial value is selected, vertex v is shifted, introduce taboo list is updated, executes next superledge.The present invention takes into account this factor of time in algorithm, can quickly judge each subgraph whether load balancing or whether the power of cutting is approximate minimum between subgraph, final purpose is to be very significantly improved the operational efficiency of distributed system.
Description
Technical field
The present invention relates to a kind of taboo search methods that time-based Large Scale Graphs equilibrium k is divided, for promoting distribution
The operational efficiency of formula system.
Background technique
Vertex v is transferred to target partition using the strategy on transfer vertex by LGEPTS algorithm, is selected in an iterative process most
Excellent solution.However do not account for iteration and need to expend duration, the runing time of the superledge in BSP model is not accounted for yet, it can be tight
Ghost image rings the efficiency of distributed system.
Summary of the invention
Goal of the invention: for the problem that LGEPTS algorithm time overhead is larger, time factor is introduced, one kind is proposed and is based on
The tabu search algorithm that the Large Scale Graphs equilibrium k of time is divided.During the algorithm is run by monitoring when the operation of each superledge
Between, according to the size of the difference of runing time and average time, find out the unbalanced reason of runing time.Subregion calculating is too long, this
When by vertex transition strategy, calculating balance factor keeps scoring area inner vertex number balanced, calculates the time so as to shorten subregion；Communication
Overlong time calculates vertex financial value by vertex transition strategy, selects the maximum subregion of vertex financial value, vertex is shifted
Into the subregion, the subgraph after dividing is finally obtained.LGEPTS-time algorithm carries out temporal optimization to LGEPTS algorithm, mentions
The operational efficiency of distributed system has been risen, the efficiency of parallel computation can be also improved.
Technical solution: analyzing original LGEPTS algorithm, due to algorithm every time require transfer vertex come guarantee divide quality,
The plenty of time can be consumed, causes the speed of service of entire superledge slack-off.This factor of time is added to Large Scale Graphs equilibrium k to draw
In the tabu search algorithm divided, a kind of taboo search method (A Tabu that time-based Large Scale Graphs equilibrium k is divided is proposed
Search Algorithm for Large Scale Equalization K Partition based on Time, brief note
For LGEPTS-time).
A kind of taboo search method that time-based Large Scale Graphs equilibrium k is divided, this method pass through in monitoring BSP model
The runing time of each superledge finds out the unbalanced reason of runing time according to the size of the difference of runing time and average time.
If subregion calculating is too long, at this time by vertex transition strategy, calculating balance factor keeps scoring area inner vertex number balanced, to contract
Short subregion calculates the time；If call duration time is too long, by vertex transition strategy, vertex financial value is calculated, selects vertex income
It is worth maximum subregion, vertex is transferred into the subregion.Taboo search method is a kind of heuristic, and this method can imitate people
The memory function of class.Vertex repeats to move back and forth between subgraph in order to prevent, which constrains extra repetition using taboo list
Operation, avoid unnecessary circulate operation as far as possible.In addition to this, by the time, this factor takes into account in algorithm this method, energy
Quickly judge whether each subgraph load balancing or cut that power is approximate minimum, and final purpose is will be distributed between subgraph
The operational efficiency of system is very significantly improved, and carries out temporal optimization to original LGEPTS algorithm.
For in BSP model, the runing time of superledge influences the distributed efficiency of whole system, and solution is designed in terms of the time
Certainly thinking: monitoring the runing time of superledge, selects corresponding vertex transition strategy according to local computing time and call duration time.
Step 1: calculating and counts each partition running time
System carries out figure calculating centered on each vertex, show that the runing time that figure calculates is such as public according to BSP model
Shown in formula (3-1):
RunT=Ts1+Ts2+...+Tsn=∑ Tsi (3-1)
The runing time that figure calculates is equal to the running time T of each superledgesiThe sum of, the runing time of each superledge is equal to institute
There is partition running time TDiMaximum value such as formula (3-2) shown in:
Tsi=max (TDi) (3-2)
The running time T of each subregionDiThe sum of time cpT and call duration time ccT are calculated equal to subregion, such as formula (3-3)
It is shown:
TDi=cpT+ccT (3-3)
So shown in the runing time such as formula (3-4) that a figure calculates:
Step 2: partition running time T is calculatedDiIllustrate point with the difference of average operating time if difference is less than threshold value
Area's runing time is within the acceptable range, if difference is greater than threshold value, jump procedure three.
Step 3: difference is greater than threshold value, illustrates to need to shift vertex, to reduce local computing time or call duration time,
To reduce the partition running time.It is divided into two kinds of situations below: first is that subregion, which calculates the time, is greater than subregion calculating average time, then
Subregion calculates the too long jump procedure four of time cpT, second is that call duration time is greater than communication average time, then call duration time ccT is too long
Jump procedure six.
Step 4: subregion calculating is too long, needs that the vertex v most with target partition neighbours' number is selected to shift, calculates
Vertex v is transferred to the balance factor e after target partition, and balance factor e can embody the balanced situation of figure by numerical value, such as public
Shown in formula 3-5:
Wherein, VoiIt is the number of vertex of sub-district after shifting vertex v, VDiIt is the summation of subregion number of vertex in entire superledge, k
It is the number of subregion,It is the ideally number of vertices of each subregion.
If shifting the balance factor behind vertex is less than the balance factor before transfer, introduce taboo list is updated, under execution
One superledge, otherwise jump procedure five.
Step 5: selecting other target partitions, and updates a barrel list, jump procedure four.
Step 6: call duration time is too long, calculates vertex v in the weights sum on the side on the vertex that original subregion is connected, calculates
The weights sum on the side on the connected vertex of target partition.
Step 7: the financial value of vertex v is calculated, the revenue function of vertex v is as shown in formula 3-6:
G (v)=Wde-Woe (3-6)
Wherein, G (v) is the revenue function that vertex v goes goal displacement sub-district from original place sub-district, WdeIt is vertex v and mesh
The weights sum on the side on all vertex connected in mark transfer sub-district, WoeWhat is connect in sub-district where being vertex v and being original owns
The weights sum on the side on vertex.
Step 8: the selection maximum sub-district of financial value shifts vertex v.
Step 9: introduce taboo list is updated, next superledge is executed.
The basic goal of figure partitioning algorithm is exactly the runing time that reduction figure calculates, and LGEPTS-time method passes through monitoring
The runing time of each superledge during system is run is found out when the runing time of superledge differs greatly with average operating time
The too long reason of runing time, shifts vertex according to local computing time or call duration time, realizes the load balancing of by stages,
Inter-partition communication is reduced simultaneously to reduce the waiting time.
Detailed description of the invention
Fig. 1 is LGEPTS-time method flow diagram；
Fig. 2 is load balancing variation diagram；
Fig. 3 is runing time figure.
Specific embodiment
Combined with specific embodiments below, the present invention is furture elucidated, it should be understood that these embodiments are merely to illustrate the present invention
Rather than limit the scope of the invention, after the present invention has been read, those skilled in the art are to various equivalences of the invention
The modification of form falls within the application range as defined in the appended claims.
Original LGEPTS algorithm is analyzed, guarantees to divide quality since algorithm requires transfer vertex every time, can consume big
The time is measured, causes the speed of service of entire superledge slack-off.This factor of time is added to the taboo of Large Scale Graphs equilibrium k division
In searching algorithm, a kind of taboo search method (A Tabu Search that time-based Large Scale Graphs equilibrium k is divided is proposed
Algorithm for Large Scale Equalization K Partition based on Time, is abbreviated as
LGEPTS-time)。
This method passes through the runing time of each superledge in monitoring BSP model, according to the difference of runing time and average time
It is worth size, finds out the unbalanced reason of runing time.The reason of influencing runing time, passes through at this time if subregion calculating is too long
Vertex transition strategy, calculating balance factor keeps scoring area inner vertex number balanced, calculates the time so as to shorten subregion；If when communication
Between it is too long, by vertex transition strategy, calculate vertex financial value, select the maximum subregion of vertex financial value, vertex is transferred into
The subregion.
By the time, this factor takes into account in method, can quickly judge each subgraph whether load balancing or whether
The power of cutting between subgraph is approximate minimum, and final purpose is to be very significantly improved the operational efficiency of distributed system, to original
LGEPTS algorithm carries out temporal optimization.
For in BSP model, the runing time of superledge influences the distributed efficiency of whole system, and solution is designed in terms of the time
Certainly thinking: monitoring the runing time of superledge, selects corresponding vertex transition strategy according to local computing time and call duration time.
Step 1: calculating and counts each partition running time
System carries out figure calculating centered on each vertex, show that the runing time that figure calculates is such as public according to BSP model
Shown in formula (3-1):
RunT=Ts1+Ts2+...+Tsn=∑ Tsi (3-1)
The runing time that figure calculates is equal to the running time T of each superledgesiThe sum of, the runing time of each superledge is equal to institute
There is partition running time TDiMaximum value such as formula (3-2) shown in:
Tsi=max (TDi) (3-2)
The running time T of each subregionDiThe sum of time cpT and call duration time ccT are calculated equal to subregion, such as formula (3-3)
It is shown:
TDi=cpT+ccT (3-3)
So shown in the runing time such as formula (3-4) that a figure calculates:
Step 2: partition running time T is calculatedDiIllustrate point with the difference of average operating time if difference is less than threshold value
Area's runing time is within the acceptable range, if difference is greater than threshold value, jump procedure three.
Step 3: difference is greater than threshold value, illustrates to need to shift vertex, to reduce local computing time or call duration time,
To reduce the partition running time.It is divided into two kinds of situations below: first is that subregion, which calculates the time, is greater than subregion calculating average time, then
Subregion calculates the too long jump procedure four of time cpT, second is that call duration time is greater than communication average time, then call duration time ccT is too long
Jump procedure six.
Step 4: subregion calculating is too long, needs that the vertex v most with target partition neighbours' number is selected to shift, calculates
Vertex v is transferred to the balance factor e after target partition, and balance factor e can embody the balanced situation of figure by numerical value, such as public
Shown in formula 3-5:
Wherein, VoiIt is the number of vertex of sub-district after shifting vertex v, VDiIt is the summation of subregion number of vertex in entire superledge, k
It is the number of subregion,It is the ideally number of vertices of each subregion.
If shifting the balance factor behind vertex is less than the balance factor before transfer, introduce taboo list is updated, under execution
One superledge, otherwise jump procedure five.
Step 5: selecting other target partitions, and updates a barrel list, jump procedure four.
Step 6: call duration time is too long, calculates vertex v in the weights sum on the side on the vertex that original subregion is connected, calculates
The weights sum on the side on the connected vertex of target partition.
Step 7: the financial value of vertex v is calculated, the revenue function of vertex v is as shown in formula 3-6:
G (v)=Wde-Woe (3-6)
Wherein, G (v) is the revenue function that vertex v goes goal displacement sub-district from original place sub-district, WdeIt is vertex v and mesh
The weights sum on the side on all vertex connected in mark transfer sub-district, WoeWhat is connect in sub-district where being vertex v and being original owns
The weights sum on the side on vertex.
Step 8: the selection maximum sub-district of financial value shifts vertex v.
Step 9: introduce taboo list is updated, next superledge is executed.
The taboo search method pseudocode that time-based Large Scale Graphs equilibrium k is divided is as follows:
Experimental verification:
Experimental section mainly in terms of two comparative experiments analysis method improvement effect, efficiency analysis and deemed-to-satisfy4
It can comparison.
1. efficiency analysis
Fig. 2 is LGEPTS algorithm and LGEPTS-time method under worker number same case, pair of load balancing e
Than figure, as seen from the figure, LGEPTS-time method is better than LGEPTS algorithm in terms of controlling load balancing.LGEPTS-time method
By detecting superledge runing time, transfer vertex realizes load balancing, there is very big improvement on original algorithm, when
When worker number gradually increases, the difference of LGEPTS-time method and the load balancing of LGEPTS algorithm can be increasing, says
The load of bright LGEPTS algorithm is more and more uneven with the increasing for number of worker.
2. algorithm performance compares
Fig. 3 is the runing time comparison diagram of LGEPTS algorithm and LGEPTS-time method each superledge in BSP model,
As seen from the figure, the entirety of the runing time of LGEPTS-time algorithm is less than the runing time of LGEPTS algorithm, logical in view of the algorithm
Monitoring runing time is crossed, equally loaded is carried out on transfer vertex, and in terms of time performance, LGEPTS-time method is calculated better than LGEPTS
Method.LGEPTS algorithm cannot rapidly judge uneven reason, need to consume plenty of time transfer vertex, divide mark to meet
It is quasi-.Leading to the runing time of each worker, equal and difference is not larger, influences the runing time of entire superledge.As can be seen that
When superledge number gradually increases, the runing time of LGEPTS-time method is stable and is less than the runing time of LGEPTS algorithm.
For in BSP model, load balancing and communication overhead inside each superledge are two essential factors, this
This factor of time is added in the tabu search algorithm of Large Scale Graphs equilibrium k division by inventive method.Pass through monitoring superledge fortune
The row time analyzes the runing time of superledge, and finds out the too long reason of runing time.Local computing is too long to be illustrated to load
Unbalanced, the too long explanation subgraph side of call duration time is cut larger.The TABU search that time-based Large Scale Graphs equilibrium k is divided is calculated
Method, which can quickly be found out, divides the undesirable reason of effect, and being reduced by TABU search this heuritic approach need not
The vertex wanted is mobile, prevents invalid movement, reduces redundancy.Finally, by experimental verification, the method for the present invention can effectively improve effect
Rate and more practicability.
Claims (5)
1. a kind of taboo search method that time-based Large Scale Graphs equilibrium k is divided, it is characterised in that: this method passes through monitoring
The runing time of each superledge in BSP model finds out runing time injustice according to the size of the difference of runing time and average time
The reason of weighing apparatus, selects corresponding vertex transition strategy.
2. the taboo search method that time-based Large Scale Graphs equilibrium k as described in claim 1 is divided, it is characterised in that:
The runing time for monitoring superledge, finds out the unbalanced reason of runing time, selects corresponding vertex transition strategy；If subregion meter
Too long, at this time by vertex transition strategy, calculating balance factor keeps scoring area inner vertex number balanced, so as to shorten subregion calculating
Time；If call duration time is too long, by vertex transition strategy, vertex financial value is calculated, selects maximum point of vertex financial value
Vertex is transferred into the subregion by area.
3. the taboo search method that time-based Large Scale Graphs equilibrium k as described in claim 1 is divided, it is characterised in that:
It calculates and counts each partition running time
The runing time that figure calculates is equal to the running time T of each superledgesiThe sum of, the runing time of each superledge is equal to all points
Area's running time TDiMaximum value such as formula (3-2) shown in:
Tsi=max (TDi) (3-2)
The running time T of each subregionDiThe sum of time cpT and call duration time ccT are calculated equal to subregion, as shown in formula (3-3):
TDi=cpT+ccT (3-3).
4. the taboo search method that time-based Large Scale Graphs equilibrium k as described in claim 1 is divided, which is characterized in that
Select corresponding vertex transition strategy process are as follows:
Step 1, partition running time T is calculatedDiIllustrate that subregion is transported if difference is less than threshold value with the difference of average operating time
The row time is within the acceptable range, if difference is greater than threshold value, jump procedure 2；
Step 2: difference is greater than threshold value, illustrates to need to shift vertex, to reduce local computing time or call duration time, to subtract
Few partition running time；It is divided into two kinds of situations below: first is that subregion calculates the too long jump procedure 3 of time cpT, second is that call duration time
The too long jump procedure 5 of ccT；
Step 3: subregion calculating is too long, needs that the vertex v most with target partition neighbours' number is selected to shift, calculates vertex v
Balance factor e after being transferred to target partition, balance factor e can embody the balanced situation of figure by numerical value, such as formula 3-5
It is shown:
Wherein, VoiIt is the number of vertex of sub-district after shifting vertex v, VDiIt is the summation of subregion number of vertex in entire superledge, k is subregion
Number,It is the ideally number of vertices of each subregion；
If shifting the balance factor behind vertex is less than the balance factor before transfer, introduce taboo list is updated, is executed next
Superledge, otherwise jump procedure 4；
Step 4: other target partitions are selected, and update a barrel list, jump procedure 3；
Step 5: call duration time is too long, calculates vertex v in the weights sum on the side on the vertex that original subregion is connected, calculates target point
The weights sum on the side on the connected vertex in area；
Step 6: the financial value of vertex v is calculated, the revenue function of vertex v is as shown in formula 3-6:
G (v)=Wde-Woe (3-6)
Wherein, G (v) is the revenue function that vertex v goes goal displacement sub-district from original place sub-district, WdeIt is that vertex v and target turn
Move the weights sum on the side on all vertex connected in sub-district, WoeIt is all vertex being connect in vertex v and original place sub-district
Side weights sum；
Step 7: the selection maximum sub-district of financial value shifts vertex v；
Step 8: updating introduce taboo list, execute next superledge.
5. the taboo search method that time-based Large Scale Graphs equilibrium k as described in claim 1 is divided, which is characterized in that
The basic goal of figure partitioning algorithm is exactly the runing time that reduction figure calculates, and this method each surpasses during being run by monitoring system
The runing time of step finds out the too long reason of runing time when the runing time of superledge differs greatly with average operating time,
Vertex is shifted according to local computing time or call duration time, realizes the load balancing of by stages, while reducing inter-partition communication
To reduce the waiting time.
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Application publication date: 20190226 |