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Journal of Combinatorial Optimization

, Volume 34, Issue 4, pp 1052–1059 | Cite as

Approximation for vertex cover in \(\beta \)-conflict graphs

  • Dongjing Miao
  • Zhipeng Cai
  • Weitian Tong
  • Jianzhong Li
Article

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 \(2-\frac{1}{2^r}\) (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 \(\beta <1\), then our algorithm will provide a \((1+\beta +\frac{1-\beta }{k})\)-approximation, where k is a parameter related to degree distribution of wheel complete multipartite graph.

Keywords

Approximation algorithm Vertex cover Conflict graph Complete multipartite graph 

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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  • Dongjing Miao
    • 1
  • Zhipeng Cai
    • 1
  • Weitian Tong
    • 2
  • Jianzhong Li
    • 3
  1. 1.Department of Computer ScienceGeorgia State UniversityAtlantaUSA
  2. 2.Department of Computer SciencesGeorgia Southern UniversityStatesboroUSA
  3. 3.School of Computer Science and TechnologyHarbin Institute of TechnologyHarbinChina

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