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An Articulation Point-Based Approximation Algorithm for Minimum Vertex Cover Problem

  • Jayanth Kumar Thenepalle
  • Purusotham SingamsettyEmail author
Conference paper
Part of the Trends in Mathematics book series (TM)

Abstract

The minimum vertex cover problem (MVCP) is a well-known NP complete combinatorial optimization problem. The aim of this paper is to present an approximation algorithm for minimum vertex cover problem (MVCP). The algorithm construction is based on articulation points/cut vertices and leaf vertices/pendant vertices. The proposed algorithm assures the near optimal or optimal solution for a given graph and can be solved in polynomial time. A numerical example is illustrated to describe the proposed algorithm. Comparative results show that the proposed algorithm is very competitive compared with other existing algorithms.

References

  1. 1.
    Garry, M., Johnson, D.: Computers and Intractability: A User Guide to the Theory of NP Completeness. San Francisco (1979)Google Scholar
  2. 2.
    Hoo, C.S., Jeevan, K., Ganapathy, V., Ramiah, H.: Variable-order ant system for VLSI multiobjective floor planning. Appl. Soft Comput. 13 (7), 3285–3297 (2013)CrossRefGoogle Scholar
  3. 3.
    Sherali, H.D., Rios, M.: An air force crew allocation and scheduling problem. J. Oper. Res. Soc. 35 (2), 91–103 (1984)CrossRefGoogle Scholar
  4. 4.
    Woodyatt, L.R., Stott, K.L., Wolf, F.E., Vasko, F.J.: An application combining setcovering and fuzzy sets to optimally assign metallurgical grades to customer orders. Fuzzy Sets Syst. 53 (1), 15–25 (1993)CrossRefGoogle Scholar
  5. 5.
    Eiter, T., Gottlob, G.: Identifying the minimal transversals of a hypergraph and related problems. SIAM J. Comput. 24 (6), 1278–1304 (1995)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Listrovoy, S., Minukhin, S.: The solution algorithms for problems on the minimal vertex cover in networks and the minimal cover in Boolean matrixes. IJCSI. 9 (5), 8–15 (2012)Google Scholar
  7. 7.
    Avis, D., Imamura, T.: A list heuristic for vertex cover. Oper. Res. Lett. 35 (2), 201–204 (2007)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Delbot, F. Laforest, C.: A better list heuristic for vertex cover. Inf. Process. Lett. 107 (3 -4), 125–127 (2008)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Savage, C.: Depth-first search and the vertex cover problem. Inf. Process. Lett. 14 (5), 233–235 (1982)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Singh, A., Gupta, A.K.: A hybrid heuristic for the minimum weight vertex cover problem. Asia-Pac. J. Oper. Res. 23, 273–285 (2006)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Vob, S., Fink, A.: A hybridized tabu search approach for the minimum weight vertex cover problem. J. Heu. 18 (6), 869–876 (2012)CrossRefGoogle Scholar
  12. 12.
    J. Chen, I.A. Kani, G. Xia, Improved upper bounds for vertex cover. Theor. Comput. Sci. 411, 3736–3756 (2010)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Tu, J.: A fixed-parameter algorithm for the vertex cover P3 problem. Inf. Process. Lett. 115 (2), 96–99 (2015)CrossRefGoogle Scholar
  14. 14.
    Shah, K., Reddy, P., Selvakumar, R.: Vertex Cover Problem - Revised Approximation Algorithm. In: Artificial Intelligence and Evolutionary Algorithms in Engineering Systems, pp. 9–16. Springer, New Delhi (2015)Google Scholar
  15. 15.
    Chen, J., Kou, L., Cui, X.: An Approximation Algorithm for the Minimum Vertex Cover Problem. Procedia Eng. 137, 180–185 (2016)CrossRefGoogle Scholar
  16. 16.
    Chen, J., Lin, Y., Li, J., Lin, G., Ma, Z., Tan, A.: A rough set method for the minimum vertex cover problem of graphs. Appl. Soft Comput. 42, 360–367 (2016)CrossRefGoogle Scholar
  17. 17.
    Hochbaum, D.S.: Approximation algorithms for the set covering and vertex cover problems. SIAM J. Comput. 11 (3), 555–556 (1982)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Dahiya, S.: A New Approximation Algorithm for Vertex Cover Problem. In: International Conference on Machine Intelligence and Research Advancement, pp. 472–478, IEEE (2013)Google Scholar
  19. 19.
    Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms. 3rd edn. MIT Press, Cambridge, MA (2009)zbMATHGoogle Scholar
  20. 20.
    Alom, B.M., Das, S., Rouf, M.A.: Performance evaluation of vertex cover and set cover problem using optimal algorithm. DUET Journal. 1 (2), (2011)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Jayanth Kumar Thenepalle
    • 1
  • Purusotham Singamsetty
    • 1
    Email author
  1. 1.Department of MathematicsVITVelloreIndia

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