Journal of Global Optimization

, Volume 59, Issue 2–3, pp 663–671 | Cite as

Minimum vertex cover in ball graphs through local search

  • Zhao Zhang
  • Weili Wu
  • Lidan Fan
  • Ding-Zhu Du


Using local search method, this paper provides a polynomial time approximation scheme for the minimum vertex cover problem on \(d\)-dimensional ball graphs where \(d \ge 3\). The key to the proof is a new separator theorem for ball graphs in higher dimensional space.


Vertex cover Ball graph Local search Separator theorem 



The work is supported by NSFC (61222201) and SRFDP (20126501110001) Xinjiang Talent Project (2013711011), and by National Science Foundation of USA under grants CNS0831579 and CCF0728851.


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.College of Mathematics and System SciencesXinjiang University UrumqiXinjiangPeople’s Republic of China
  2. 2.Department of Computer ScienceUniversity of Texas at DallasRichardsonUSA

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