Local Search with Noisy Strategy for Minimum Vertex Cover in Massive Graphs

  • Zongjie MaEmail author
  • Yi Fan
  • Kaile Su
  • Chengqian Li
  • Abdul Sattar
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9810)


Finding minimum vertex covers (MinVC) for simple undirected graphs is a well-known NP-hard problem. In the literature there have been many heuristics for obtaining good vertex covers. However, most of them focus on solving this problem in relatively small graphs. Recently, a local search solver called FastVC is designed to solve the MinVC problem on real-world massive graphs. Since the traditional best-picking heuristic was believed to be of high complexity, FastVC replaces it with an approximate best-picking strategy. However, since best-picking has been proved to be powerful for a wide range of problems, abandoning it may be a great sacrifice. In this paper we have developed a local search MinVC solver which utilizes best-picking with noise to remove vertices. Experiments conducted on a broad range of real-world massive graphs show that our proposed method finds better vertex covers than state-of-the-art local search algorithms on many graphs.


Minimum vertex cover Heuristic search Massive graphs Combinatorial optimization Social networks 



This work is supported by ARC Grant FT0991785, NSF Grant No. 61463044 and Grant No. [2014]7421 from the Joint Fund of the NSF of Guizhou province of China.


  1. 1.
    Andrade, D.V., Resende, M.G.C., Werneck, R.F.F.: Fast local search for the maximum independent set problem. J. Heuristics 18(4), 525–547 (2012)CrossRefGoogle Scholar
  2. 2.
    Barbosa, V.C., Campos, L.C.D.: A novel evolutionary formulation of the maximum independent set problem. J. Comb. Optim. 8(4), 419–437 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Cai, S.: Balance between complexity and quality: local search for minimum vertex cover in massive graphs. In: Proceedings of the Twenty-Fourth International Joint Conference on Artificial Intelligence, IJCAI, pp. 25–31 (2015)Google Scholar
  4. 4.
    Cai, S., Su, K., Chen, Q.: EWLS: a new local search for minimum vertex cover. In: AAAI (2010)Google Scholar
  5. 5.
    Cai, S., Su, K., Luo, C., Sattar, A.: NuMVC: an efficient local search algorithm for minimum vertex cover. J. Artif. Intell. Res. 46, 687–716 (2013)MathSciNetzbMATHGoogle Scholar
  6. 6.
    Cai, S., Su, K., Sattar, A.: Local search with edge weighting and configuration checking heuristics for minimum vertex cover. Artif. Intell. 175(9), 1672–1696 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Chung Graham, F., Lu, L.: Complex graphs and networks american mathematical society (2006)Google Scholar
  8. 8.
    Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms, vol. 6. MIT Press, Cambridge (2001)Google Scholar
  9. 9.
    Eubank, S., Kumar, V., Marathe, M.V., Srinivasan, A., Wang, N.: Structural and algorithmic aspects of massive social networks. In: Proceedings of the Fifteenth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 718–727. Society for Industrial and Applied Mathematics (2004)Google Scholar
  10. 10.
    Ji, Y., Xu, X., Stormo, G.D.: A graph theoretical approach for predicting common RNA secondary structure motifs including pseudoknots in unaligned sequences. Bioinformatics 20(10), 1603–1611 (2004)CrossRefGoogle Scholar
  11. 11.
    Jin, Y., Hao, J.: General swap-based multiple neighborhood tabu search for the maximum independent set problem. Eng. Appl. AI 37, 20–33 (2015)CrossRefGoogle Scholar
  12. 12.
    Johnson, D.S., Trick, M.A.: Cliques, Coloring, and Satisfiability: Second DIMACS Implementation Challenge, vol. 26. American Mathematical Society, Providence (1996)zbMATHGoogle Scholar
  13. 13.
    Katayama, K., Hamamoto, A., Narihisa, H.: An effective local search for the maximum clique problem. Inf. Process. Lett. 95(5), 503–511 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Li, C.M., Quan, Z.: An efficient branch-and-bound algorithm based on maxsat for the maximum clique problem. In: Proceedings of the Twenty-Fourth AAAI Conference on Artificial Intelligence, AAAI 2010, vol. 10, pp. 128–133. AAAI Press, Atlanta (2010)Google Scholar
  15. 15.
    Pullan, W.J., Hoos, H.H.: Dynamic local search for the maximum clique problem. J. Artif. Intell. Res. (JAIR) 25, 159–185 (2006)zbMATHGoogle Scholar
  16. 16.
    Richter, S., Helmert, M., Gretton, C.: A stochastic local search approach to vertex cover. In: Hertzberg, J., Beetz, M., Englert, R. (eds.) KI 2007. LNCS (LNAI), vol. 4667, pp. 412–426. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  17. 17.
    Rossi, R., Ahmed, N.: The network data repository with interactive graph analytics and visualization. In: AAAI, pp. 4292–4293 (2015)Google Scholar
  18. 18.
    Rossi, R.A., Ahmed, N.K.: Coloring large complex networks. Soc. Netw. Anal. Min. 4(1), 1–37 (2014)CrossRefGoogle Scholar
  19. 19.
    Rossi, R.A., Gleich, D.F., Gebremedhin, A.H., Patwary, M.M.A.: Fast maximum clique algorithms for large graphs. In: Proceedings of the Companion Publication of the 23rd International Conference on World Wide Web Companion, pp. 365–366. International World Wide Web Conferences Steering Committee (2014)Google Scholar
  20. 20.
    Segundo, P.S., Rodríguez-Losada, D., Jiménez, A.: An exact bit-parallel algorithm for the maximum clique problem. Comput. OR 38(2), 571–581 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Traud, A.L., Mucha, P.J., Porter, M.A.: Social structure of facebook networks. Phys. A Stat. Mech. Appl. 391(16), 4165–4180 (2012)CrossRefGoogle Scholar
  22. 22.
    Wu, Q., Hao, J.K.: A review on algorithms for maximum clique problems. Eur. J. Oper. Res. 242(3), 693–709 (2015)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Zongjie Ma
    • 1
    Email author
  • Yi Fan
    • 1
  • Kaile Su
    • 1
  • Chengqian Li
    • 2
  • Abdul Sattar
    • 1
  1. 1.Institute for Integrated and Intelligent SystemsGriffith UniversityBrisbaneAustralia
  2. 2.Department of Computer ScienceSun Yat-sen UniversityGuangzhouChina

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