Advertisement

Vertex Cover Problem—Revised Approximation Algorithm

  • Kartik Shah
  • Praveenkumar Reddy
  • R. Selvakumar
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 324)

Abstract

This paper is aimed to present the solution to vertex cover problem by means of an approximation solution. As it is NP complete problem, we can have an approximate time algorithm to solve the vertex cover problem. We will modify the algorithm to have an algorithm which can be solved in polynomial time and which will give near to optimum solution. It is a simple algorithm which will be based on articulation point. Articulation point can be found using the Depth First Search algorithm.

Keywords

Articulation point Vertex covering problem Optimization Approximation algorithm 

Notes

Acknowledgment

We would like to thank the School of Computer Science and Engineering, VIT University, for giving us such an opportunity to carry out this research work and also for providing us the requisite resources and infrastructure for carrying out the research.

References

  1. 1.
    M. Garry, D. Johnson, Computers and Intractability: A User Guide to the Theory of NP Completeness (San Francisco, 1979)Google Scholar
  2. 2.
    P.S. Oliveto, X. Yao, J. He, Analysis of Population-based Evolutionary Algorithms for the Vertex Cover Problem (IEEE, 2008), pp. 1563–1570Google Scholar
  3. 3.
    L. Ding, B. Gu, X. Hong, B. Dixon, Articulation node based routing in delay tolerant networks, in IEEE International Conference (2009), pp. 1–6Google Scholar
  4. 4.
    Y. Zeng, D. Wang, W. Liu, A. Xiong, An approximation algorithm for weak vertex cover problem in IP network traffic measurement, IEEE International Conference (2009), pp. 182–186Google Scholar
  5. 5.
    J. Chen, I.A. Kanj, G. Xia, Improved parameterized upper bounds for vertex cover. 31st International Conference on Mathematical Foundations of Computer Science (2006)Google Scholar
  6. 6.
    F. Delbot, C. Laforest, A better list heuristic for vertex cover. Inf. Process. Lett. 107, 125–127 (2008)CrossRefMATHMathSciNetGoogle Scholar
  7. 7.
    E. Angel, R. Campigotto, C. Laforest, Algorithm for the vertex cover problem on large graphs. IBISC Research report (2010)Google Scholar
  8. 8.
    R. Bar-Yehuda, S. Even, A local-ratio theorem for approximating the weighted vertex cover problem. Ann. Discrete Math. 25, 27–46 (1985)MathSciNetGoogle Scholar
  9. 9.
    G.L. Nemhauser, L.E. Trotter, Vertex packing: structural properties and algorithms. Math. Program. 8, 232–248 (1975)CrossRefMATHMathSciNetGoogle Scholar
  10. 10.
    E. Asgeirsson, C. Stein, Vertex Cover Approximations on Random Graphs (Springer, Berlin, 2007), pp. 285–296Google Scholar
  11. 11.
    P. Erdos, A. Renyi, On random graphs. Publ. Math. Debrecen 6, 290–297 (1959)MathSciNetGoogle Scholar
  12. 12.
    F. Kuhn, M. Mastrolilli, Vertex cover in graphs with locally few colors (2011), pp 498–509 Google Scholar
  13. 13.
    D. Hochbaum, Approximation algorithms for the set covering and vertex cover problems. SIAM J. Comput. 11(3), 555–556 (1982)CrossRefMATHMathSciNetGoogle Scholar

Copyright information

© Springer India 2015

Authors and Affiliations

  • Kartik Shah
    • 1
  • Praveenkumar Reddy
    • 1
  • R. Selvakumar
    • 1
  1. 1.School of Computing Science and EngineeringVIT UniversityVelloreIndia

Personalised recommendations