| 76 | 0 | 51 |
| Downloads | Citas | Reads |
In the weighted undirected graph with high density and complex structure, due to the complex information transfer, the traditional information propagation algorithm was less efficient to solve the maximum weighted clique problem. Using the mapping relationship between the maximum weight independent set and the maximum weight clique, an algorithm was proposed to solve the maximum weight group problem for high-density weighted undirected graphs. The propagation algorithm was combined with the iterative equation to design the potential function of the information propagation algorithm. At the same time, the weighted undirected graph of the high-density complex structure was mapped into a factor graph, and the deloop operation was performed, and the feature convergence calculation was performed by iterative information propagation, and the optimal solution of the maximum weight group was calculated by the maximum posterior probability after iterative convergence. Experimental results were compared and analyzed based on random graphs with different densities. The results showed that the algorithm was very effective in solving the maximum weight problem of weighted undirected graphs with high-density complex structures, and the accuracy and speed of solving the total weights were higher than those of the standard belief propagation algorithm.
[1] 仲盛，谢立.求解图的最大团的一种算法[J].软件学报，1999,10(3):288-292.ZHONG S,XIE L.An algorithm computing the maximum clique in a graph[J].Journal of software,1999,10(3):288-292.
[2] YU Z,WANG X F,ZHAO J.A local dense decision-making method for solving the maximum clique problem in large-scale undirected graphs[J].Computers and electrical engineering,2022,102:108220.
[3] SHIMIZU S,YAMAGUCHI K,MASUDA S.Parallelization of a branch-and-bound algorithm for the maximum weight clique problem[J].Discrete optimization,2021,41:100646.
[4] MENG X M,XIANG J,ZHENG R Q,et al.DPCMNE:detecting protein complexes from protein-protein interaction networks via multi-level network embedding[J].IEEE/ACM transactions on computational biology and bioinformatics,2022,19(3):1592-1602.
[5] GSCHWIND T,IRNICH S,FURINI F,et al.A branch-and-price framework for decomposing graphs into relaxed cliques[J].Informs journal on computing,2021,33(3):1070-1090.
[6] SHIROKANEV A,ILYASOVA N,DEMIN N,et al.Extracting a DME area based on graph-based image segmentation and collation of OCT retinal images[J].Journal of physics:conference series,2021,1780:012031.
[7] SHU Y C,ZHANG J,XIAO B,et al.Medical image segmentation based on active fusion-transduction of multi-stream features[J].Knowledge-based systems,2021,220:106950.
[8] 江华.最大团问题精确算法研究[D].武汉：华中科技大学，2017.JIANG H.On exact algorithms for the maximum clique problem[D].Wuhan:Huazhong University of Science and Technology,2017.
[9] ?STERG?RD P R J.A fast algorithm for the maximum clique problem[J].Discrete applied mathematics,2002,120(1/2/3):197-207.
[10] KUMLANDER D.On importance of a special sorting in the maximum-weight clique algorithm based on colour classes[C]//International Conference on Modelling,Computation and Optimization in Information Systems and Management Sciences.Berlin:Springer Press,2008:165-174.
[11] LI C M,LIU Y L,JIANG H,et al.A new upper bound for the maximum weight clique problem[J].European journal of operational research,2018,270(1):66-77.
[12] WALTEROS J L,BUCHANAN A.Why is maximum clique often easy in practice?[J].Operations research,2020,68(6):1866-1895.
[13] NOGUEIRA B,PINHEIRO R G S.A CPU-GPU local search heuristic for the maximum weight clique problem on massive graphs[J].Computers & operations research,2018,90:232-248.
[14] EL BAZ D,HIFI M,WU L,et al.A parallel ant colony optimization for the maximum-weight clique problem[C]//IEEE International Parallel and Distributed Processing Symposium Workshops.Piscataway:IEEE Presss,2016:796-800.
[15] PATTABIRAMAN B,ALI PATWARY M M,GEBREMEDHIN A H,et al.Fast algorithms for the maximum clique problem on massive sparse graphs[C]//International Workshop on Algorithms and Models for the Web-graph.Cham:Springer International Publishing,2013:156-169.
[16] YEDIDIA J S,FREEMAN W T,WEISS Y.Understanding belief propagation and its generalizations[J].Intelligence,2002,8:236-239.
[17] 吴宇翔，王晓峰，丁红胜，等.一种改进的警示传播算法求解Max-SAT问题[J].计算机应用研究，2022,39(8):2290-2294.WU Y X,WANG X F,DING H S,et al.Improved warning propagation algorithm for solving Max-SAT problem[J].Application research of computers,2022,39(8):2290-2294.
[18] 张丹丹，王晓峰，冯琬晶，等.一种求解0-1背包问题的置信传播算法[J].郑州大学学报(理学版),2021,53(1):29-34.ZHANG D D,WANG X F,FENG W J,et al.A belief propagation algorithm for 0-1 knapsack problem[J].Journal of Zhengzhou university (natural science edition),2021,53(1):29-34.
[19] 程亚南，王晓峰，刘凇佐，等.一种求解旅行商问题的信息传播算法[J].郑州大学学报(理学版),2022,54(3):52-58.CHENG Y N,WANG X F,LIU S Z,et al.An information propagation algorithm for solving traveling salesman problem[J].Journal of Zhengzhou university (natural science edition),2022,54(3):52-58.
[20] SANGHAVI S,MALIOUTOV D,WILLSKY A.Belief propagation and LP relaxation for weighted matching in general graphs[J].IEEE transactions on information theory,2011,57(4):2203-2212.
[21] CORNELISSEN K,MANTHEY B.Belief propagation for the maximum-weight independent set and minimum spanning tree problems[J].Theoretical computer science,2018,738:53-64.
[22] 王晓峰，于卓，赵健，等.大规模图例的最大团问题算法分析[J].计算机工程，2022,48(6):182-192,199.WANG X F,YU Z,ZHAO J,et al.Algorithm analysis for solving maximum clique problems of large-scale graphs[J].Computer engineering,2022,48(6):182-192,199.
[23] VIGAN I.Understanding belief propagation dialects and their application to optimization problems[D].Zurich:Swiss Federal Institute of Technology,2009.
[24] SHA J,LIU J B,LIN J,et al.A stage-combined belief propagation decoder for polar codes[J].Journal of signal processing systems,2018,90(5):687-694.
[25] PARK S,SHIN J.Max-product belief propagation for linear programming:applications to combinatorial optimization[EB/OL].(2014-12-16)[2022-03-15].https://arxiv.org/abs/1412.4972.
[26] PARK S,SHIN J.Convergence and correctness of max-product belief propagation for linear programming[J].SIAM journal on discrete mathematics,2017,31(3):2228-2246.
[27] 王向阳，张源.一种改进的分布式最大权独立集算法[J].电子与信息学报，2012,34(3):689-693.WANG X Y,ZHANG Y.An improved distributed algorithm for maximum weight independent set(MWIS) problem[J].Journal of electronics & information technology,2012,34(3):689-693.
[28] 杜鹏.一种启发式的分布式最大独立集算法[J].南京邮电大学学报(自然科学版),2013,33(6):18-23,28.DU P.A heuristic distributed algorithm for the maximum weight independent set problem[J].Journal of Nanjing university of posts and telecommunications (natural science),2013,33(6):18-23,28.
[29] SANGHAVI S,SHAH D,WILLSKY A S.Message passing for maximum weight independent set[J].IEEE transactions on information theory,2009,55(11):4822-4834.
[30] NIEBERG T,HURINK J.Wireless communication graphs[C]//Proceedings of the Intelligent Sensors,Sensor Networks and Information Processing Conference.Piscataway:IEEE Press,2005:367-372.
Basic Information:
DOI：10.13705/j.issn.1671-6841.2022247
China Classification Code:TP18;O157.5
Citation Information:
[1]YU Zhuo,WANG Xiaofeng,WU Yuxiang ,et al.An Information Propagation Algorithm for Solving High-density Maximum Weight Groups[J].Journal of Zhengzhou University(Natural Science Edition),2024,56(04):56-64.DOI:10.13705/j.issn.1671-6841.2022247.
Fund Information:
国家自然科学基金项目(62062001,61962002); 宁夏自然科学基金项目(2020AAC03214); 北方民族大学重大专项(ZDZX201901)
2023-08-04
2023-08-04
2023-08-04