CN107729644A - It is a kind of that the method for improving available time and realizing minimum dominant set is calculated using film - Google Patents
It is a kind of that the method for improving available time and realizing minimum dominant set is calculated using film Download PDFInfo
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- CN107729644A CN107729644A CN201710942136.8A CN201710942136A CN107729644A CN 107729644 A CN107729644 A CN 107729644A CN 201710942136 A CN201710942136 A CN 201710942136A CN 107729644 A CN107729644 A CN 107729644A
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Abstract
The present invention relates to a kind of method for being calculated using film and improving available time and realizing minimum dominant set, comprise the following steps：Establish film and calculate (P system) MDS (minimum dominant set) model；Initialize the film computing unit for realizing MDS；Define the quantity of film computing unit；Linear representation is inputted into film computing unit；Combination algorithm, iteration performs under P Lingua environment, it is to calculate to complete a kind of method for realizing minimum dominant set using film that the MDS. present invention calculated based on film is finally realized in linear session, shown by the result of embodiment, available time is the method increase, solves the problems, such as the efficient algorithm that minimum dominant set is solved in linear session.
Description
Technical field：
The invention belongs to the optimizing research field that film calculates, Dominating set problem in graph theory is designed into, is more specifically
A kind of calculated using film improves the minimum method only with collection of available time realization.
Background technology：
Match somebody with somebody one of the subject matter of collection (MDS) as graph-theoretical algorithm for minimum especially has substantial amounts of answer in figure excavates
With, the problem of due to it being NP-hard approximate solution MDS, many work be directed to always center for limiting figure class and point
Cloth approximate data.The minimum dominant set of figure, using TABU search, genetic algorithm etc., can finally be looked in terms of algorithm realization
To minimum dominant set, acquired results are compared, radix minimum is exactly minimum dominant set.But as above method is used, it is counted
Evaluation time complexity is exponential, is difficult to realize when nodes are larger.It is minimum there is presently no being solved in specific linear session
The efficient algorithm of dominant set.Therefore, the new method for being introduced as the MDS for solving the problems, such as linear session is an of great value work
Make.Film calculate be Natural computation field it is new point it, be the computation model taken out from biological cell, the model is in multinomial
Time interior energy effectively solves the problems, such as correlation computations difficulty.The present invention makes full use of the concurrency feature of membranous system, it is proposed that Yi Zhongli
The method for improving available time and realizing minimum dominant set is calculated with film.
The content of the invention
To solve the above problems, film is calculated (P systems by the present invention to realize that minimum dominant set (MDS) devises a kind of method
System) thought is incorporated into the invention, it is proposed that solve the problems, such as MDS film algorithm in linear session using film algorithm.
The scheme that the present invention solves the above problems：It is proposed that one kind calculates raising available time using film and realizes that minimum dominates
The method of collection,
Specifically include following steps：Establish film and calculate (P system) MDS models, method is as follows：
The MDS models calculated based on film are defined, if figure G=(V, E), wherein V represent figure summit and include the collection on m summit
Close, E represents set while n bars, defines P system Π=(O, H, w that MDS is completed in linear session1,w2,...,
wq, R), (set linear session to be expressed as：), am+bn+c. comprise the following steps that in detail：
1st step：If the degree of P system is q, q is the natural number more than 1.
2nd step：Object Character collection O in MDS is defined with reference to the principle of graph theory and MDS, specific character definition is：
Nodes in m representative graphs；
Nonoriented edge number in n representative graphs；
XiRepresent node i；
Xi' represent domination node or adjacent domination node；
diRepresent and dominate node；
ndiRepresent non-dominant node；
upcountDiIt is minimum in film to dominate a few collection counter incrementings；
Di diIn upcountDiValue after change；
XijRepresent the side between node i and j；
countDiCounter follows the increase of dominant set nodes in film and increased；
countoutiExpression of the object in dominant set in film；
count1iRepresent regular counter in control film；
count2iRepresent the counter that membrane marker is produced by rule in film；
count3iRepresent regular caused film production method counter；
count4iControl sends film production method step；
The Z objects are consumed, and are retained in film and dominated diversity method, ultimately generate countouti；
This object of Y is consumed after produced film；
MDSiRepresent possible minimum dominant set body；
O can be defined as by above-mentioned；O={ { Di,Xi,Xi',di,ndi}∪{Xij}∪{countDi,countouti}∪
{count1i,count2i,count3i,count4i}∪{upcountDi,Z,Y}∪{MDSi}.
3rd step：Mark of the definition comprising n film is { 1,2 ..., n } membrane structure u=[[]1,[]2...[]n-1]0.
H=2 is taken, with reference to the definition of the 1st step, then the multiset in 2 regions is:w2={ Xi}∪{Xij}∪{count10,count20,
count30,Z}w1={ count00, wherein w1,w2For the character string in O.
4th step：Distribute, communicate in the i of region in u, evolutionary rule R is defined as：
r1i≡[Xi]2→[di]2[ndi]2；
r2i≡[di→DiupcountDi]2；
r3i≡[countDIupcountDi→countDi+1]2；
r4i≡[count1i→count1i+1]2；
r5i≡[count2i→count2i+1]2；
r6i≡[count3i→count3i+1]2；
r7i≡[count1i+1]2→[]2count1i+1；
r8i≡[DiXij→DiX'j]2；
r9i≡[DiXji→DiX'j]2；
r10i≡[count2i→count2i+1]2；
r11i≡[count3i→count3i+1]2；
r12i≡[count2am+bn+c→Y]2；
r13i≡[ZXijY→Xij]2；
r14i≡[ZcountDicount3am+bn+c→countouti]2；
r15i≡[countouti]2→[]2countouti；
r16i≡[count4i→count4i+1]1；
r17i≡[countouticountoutj→countouti]1；
r18i≡[countouticount4am+bn+c→MDSi]1；
r19i≡[MDSi]1→[]1MDSi；
In above-mentioned strictly all rules, all variables are taken the numerical value in zone of reasonableness by concrete case.Using above-mentioned Different Rule,
By setting different step numbers, finally minimum possible outcome is discharged into environment, solved in linear session (am+bn+c)
MDS problems.
Brief description of the drawings
Fig. 1 is implementation method flow chart of steps of the present invention；
Fig. 2 is Simulation results of the present invention；
Embodiment
It is described below in conjunction with the principle to the present invention and method, illustrates and be served only for explaining the present invention, be not intended to
Limit the scope of the present invention；
With reference to foregoing invention content, it is assumed that it is 4 × 4 matrixes (m=4, n=3) to build non-directed graph, and makes a=1, b=2, c
=0. is specifically divided into 2 stages completions.
1st stage：It is 2 cells the cell division labeled as 2, by iteration, is terminated to issuable candidate solution,
Meanwhile 4 counters determine the time started and counting unit is set as 1 respectively, rule performs parallel in respective film.Tool
Body includes the following steps：
1st step：Initialization counter and object set are as follows：
[[ZX1X2X12X3X23count10count20count30countD0]2count40]1
2nd step：Label film is split into 2 films using rule, unison counter value also follows change：
[[Zd1X2X12X3X23count11count21count31countD0]2
[Znd1X2X12X3X23count11count21count31countD0]2count41]1
3rd step：UpcountD is generated using rulei, change d in filmi：
[[ZD1d2X12X3X23upcountDcount12count22count32countD0]2
[ZD1nd2X12X3X23upcountDcount12count22count32countD0]2
[Znd1d2X12X3X23count12count22count32countD0]2
[Znd1nd2X12X3X23count12count22count32countD0]2count41]1
4th step：D is generated using rule2, with countDiIncrease：
[[Znd1D2X12X3X23upcountDcount13count23count33countD0]2
[Znd1nd3X12D2X23upcountDcount13count23count33countD0]2
[Znd1nd2X12d3X23count13count23count33countD0]2
[Znd1nd2X12nd3X23count13count23count33countD0]2
[ZD1D2X12X3X23upcountDcount13count23count33countD0]2
[ZD1D2nd3X12X23upcountDcount13count23count33countD0]2
[ZD1nd2d3X12X23count13count23count33countD0]2
[ZD1nd2nd3X12X23count13count23count33countD0]2
count43]1
5th step：Respective rule is continued executing with 2 films that division obtains：
[[Znd1D2X12D3X23upcountDcount14count24count34countD1]2
[Znd1nd3X12D2X23upcountDcount14count24count34countD0]2
[Znd1D2X12nd3X23count14count24count34countD1]2
[Znd1nd2X12nd3X23count14count24count34countD0]2
[ZD1D2X12D3X23upcountDcount14count24count34countD2]2
[ZD1D3nd2X12X23upcountDcount14count24count34countD1]2
[ZD1nd3D2X12X23count14count24count34countD2]2
[ZD1nd2nd3X12X23count14count24count34countD1]2
count44]1
6th step：Belong to the node for dominating collective with reference to whether linear representation predicate node belongs to dominant set or be connected to：
[[ZD1D3nd2X'2X'2countD2count25count35]2
[ZD1nd3nd2X'2X'23countD1count25count35]2
[ZD1D2D3X'2X3'countD3count25count35]2
[ZD1D2nd3X'2X3'countD2count25count35]2
[Znd1nd2D3X12X'2countD1count25count35]2
[Znd1nd2nd3X12X23countD0count25count35]2
[ZD1nd1D2X'2X3'countD2count25count35]2
[Znd1nd3D2X'2X'23countD1count25count35]2
count45(count14)8]1
7th step:Y is produced, consumes count2：
[[ZD1D3nd2X'2X'2countD2Ycount36]2
[ZD1nd3nd2X'2X'23countD1Ycount36]2
[ZD1D2D3X'2X3'countD3Ycount36]2
[ZD1D2nd3X'2X3'countD2Ycount36]2
[Znd1nd2D3X12X'2countD1Ycount36]2
[Znd1nd2nd3X12X23countD0Ycount36]2
[ZD1nd1D2X'2X3'countD2Ycount36]2
[Znd1nd3D2X'2X'23countD1Ycount36]2
count46(count14)8]1
8th step：Produce the film in the absence of dominant set element：
[[ZD1D3nd2X'2X'2countD2Ycount37]2
[ZD1nd3nd2X'2X'23countD1count37]2
[ZD1D2D3X'2X3'countD3Ycount37]2
[ZD1D2nd3X'2X3'countD2Ycount37]2
[Znd1nd2D3X12X'2countD1count37]2
[Znd1nd2nd3X12X23countD0count37]2
[ZD1nd1D2X'2X3'countD2Ycount37]2
[Znd1nd3D2X'2X'23countD1Ycount37]2
count47(count14)8]1
9th step：Using rule set, countout is produced：
[[D1D3nd2X'2X'2Ycountout2]2
[D1nd3nd2X'2X'23countD1count37]2
[D1D2D3X'2X3'countout3Y]2
[D1D2nd3X'2X3'countout2Y]2
[nd1nd2D3X12X'2countD1count37]2
[nd1nd2nd3X12X23countD0count37]2
[D1nd1D2X'2X3'countout2Y]2
[nd1nd3D2X'2X'23countout1Y]2
count48(count14)8]1
10th step：It can be obtained using defined rule of communication：
[[D1D3nd2X'2X'2Ycountout2]2
[D1nd3nd2X'2X'23countD1count37]2
[D1D2D3X'2X3'countout3Y]2
[D1D2nd3X'2X3'countout2Y]2
[nd1nd2D3X12X'2countD1count37]2
[nd1nd2nd3X12X23countD0count37]2
[D1nd1D2X'2X3'countout2Y]2
[nd1nd3D2X'2X'23countout1Y]2
count49(count14)8countout1countout2countout2countout3]1
2nd stage：As a result export.
By above-mentioned execution step number, making full use of in the case of definition rule set, under P-Lingua simulated environment
The simulation result of realization is as shown in Figure 2.
Claims (6)
1. a kind of calculated using film improves the available time method of realizing minimum dominant set, it is characterised in that specifically include with
Lower step：
Step 1：Establish film and calculate (P system) MDS models；
Step 2：Initialize the film computing unit for realizing MDS；
Step 3：Define the quantity of film computing unit；
Step 4：Linear representation is inputted into film computing unit；
Step 5：Combination algorithm, iteration are performed, and the MDS calculated based on film is finally realized in linear session.
2. according to claim 1 calculate the method for improving available time and realizing minimum dominant set, its feature using film
It is：The MDS models calculated based on film are defined, if figure G=(V, E), wherein V represent figure summit and include the collection on m summit
Close, E represents set while n bars, defines P system Π=(O, H, w that MDS is completed in linear session1,w2,...,
wq, R).
3. according to claim 1 calculate the method for improving available time and realizing minimum dominant set, its feature using film
It is：Object Character collection O in MDS is defined with reference to the principle of graph theory and MDS, specific character definition is：
Nodes in m representative graphs；
Nonoriented edge number in n representative graphs；
XiRepresent node i；
X′iRepresent and dominate node or adjacent domination node；
diRepresent and dominate node；
ndiRepresent non-dominant node；
upcountDiIt is minimum in film to dominate a few collection counter incrementings；
Di diIn upcountDiValue after change；
XijRepresent the side between node i and j；
countDiCounter follows the increase of dominant set nodes in film and increased；
countoutiExpression of the object in dominant set in film；
count1iRepresent regular counter in control film；
count2iRepresent the counter that membrane marker is produced by rule in film；
count3iRepresent regular caused film production method counter；
count4iControl sends film production method step；
The Z objects are consumed, and are retained in film and dominated diversity method, ultimately generate countouti；
This object of Y is consumed after produced film；
MDSiRepresent possible minimum dominant set body；
O can be defined as by above-mentioned；O={ { Di,Xi,X′i,di,ndi}∪{Xij}∪{countDi,countouti}∪
{count1i,count2i,count3i,count4i}∪{upcountDi,Z,Y}∪{MDSi}。
4. according to claim 1 calculate the method for improving available time and realizing minimum dominant set, its feature using film
It is：Mark of the definition comprising n film is { 1,2 ..., n } membrane structure u=[[]1,[]2...[]n-1]0H=2 is taken, is weighed
Profit requires 2, if the multiset in 2 regions is:w2={ Xi}∪{Xij}∪{count10,count20,count30,Z}w1=
{count00, wherein w1,w2For the character string in O.
5. according to claim 1 calculate the method for improving available time and realizing minimum dominant set, its feature using film
It is：Distribute, communicate in the i of region, evolutionary rule R is defined as：
r1i≡[Xi]2→[di]2[ndi]2；
r2i≡[di→DiupcountDi]2；
r3i≡[countDIupcountDi→countDi+1]2；
r4i≡[count1i→count1i+1]2；
r5i≡[count2i→count2i+1]2；
r6i≡[count3i→count3i+1]2；
r7i≡[count1i+1]2→[]2count1i+1；
r8i≡[DiXij→DiX'j]2；
r9i≡[DiXji→DiX'j]2；
r10i≡[count2i→count2i+1]2；
r11i≡[count3i→count3i+1]2；
r12i≡[count2am+bn+c→Y]2；
r13i≡[ZXijY→Xij]2；
r14i≡[ZcountDicount3am+bn+c→countouti]2；
r15i≡[countouti]2→[]2countouti；
r16i≡[count4i→count4i+1]1；
r17i≡[countouticountoutj→countouti]1；
r18i≡[countouticount4am+bn+c→MDSi]1；
r19i≡[MDSi]1→[]1MDSi。
6. according to claim 1 calculate the method for improving available time and realizing minimum dominant set, its feature using film
It is：All variables are taken the numerical value in zone of reasonableness by concrete case.Using Different Rule collection, by setting different step numbers,
Finally minimum possible outcome is discharged into environment, solves the problems, such as MDS in linear session (am+bn+c).
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN108648206A (en) * | 2018-04-28 | 2018-10-12 | 成都信息工程大学 | A kind of Robert edge detections film computing system and method |
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN108648206A (en) * | 2018-04-28 | 2018-10-12 | 成都信息工程大学 | A kind of Robert edge detections film computing system and method |
| CN108648206B (en) * | 2018-04-28 | 2022-09-16 | 成都信息工程大学 | Robert edge detection film computing system and method |
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