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Approximation for vertex cover in $$\beta $$ β -conflict graphs

Author

Listed:
  • Dongjing Miao

    (Georgia State University)

  • Zhipeng Cai

    (Georgia State University)

  • Weitian Tong

    (Georgia Southern University)

  • Jianzhong Li

    (Harbin Institute of Technology)

Abstract

Conflict graph is a union of finite given sets of disjoint complete multipartite graphs. Vertex cover on this kind of graph is used first to model data inconsistency problems in database application. It is NP-complete if the number of given sets r is fixed, and can be approximated within $$2-\frac{1}{2^r}$$ 2 - 1 2 r (Miao et al. in Proceedings of the 9th international conference on combinatorial optimization and applications, vol 9486. COCOA 2015, New York. Springer, New York, pp 395–408, 2015). This paper shows a better algorithm to improve the approximation for dense cases. If the ratio of vertex not belongs to any wheel complete multipartite graph is no more than $$\beta

Suggested Citation

  • Dongjing Miao & Zhipeng Cai & Weitian Tong & Jianzhong Li, 2017. "Approximation for vertex cover in $$\beta $$ β -conflict graphs," Journal of Combinatorial Optimization, Springer, vol. 34(4), pages 1052-1059, November.
    • Handle: RePEc:spr:jcomop:v:34:y:2017:i:4:d:10.1007_s10878-017-0127-z
    DOI: 10.1007/s10878-017-0127-z
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