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A 2-approximation for the maximum satisfying bisection problem

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  • Ries, Bernard
  • Zenklusen, Rico

Abstract

Given a graph G = (V, E), a satisfying bisection of G is a partition of the vertex set V into two sets V1, V2, such that |V1| = |V2|, and such that every vertex v [set membership, variant] V has at least as many neighbors in its own set as in the other set. The problem of deciding whether a graph G admits such a partition is -complete. In Bazgan et al. (2008) [C. Bazgan, Z. Tuza, D. Vanderpooten, Approximation of satisfactory bisection problems, Journal of Computer and System Sciences 75 (5) (2008) 875-883], the authors present a polynomial-time 3-approximation for maximizing the number of satisfied vertices in a bisection. It remained an open problem whether one could find a (3 - c)-approximation, for c > 0 (see Bazgan et al. (2010) [C. Bazgan, Z. Tuza, D. Vanderpooten, Satisfactory graph partition, variants, and generalizations, European Journal of Operational Research 206 (2) (2010) 271-280]). In this paper, we solve this problem by presenting a polynomial-time 2-approximation algorithm for the maximum number of satisfied vertices in a satisfying bisection.

Suggested Citation

  • Ries, Bernard & Zenklusen, Rico, 2011. "A 2-approximation for the maximum satisfying bisection problem," European Journal of Operational Research, Elsevier, vol. 210(2), pages 169-175, April.
    • Handle: RePEc:eee:ejores:v:210:y:2011:i:2:p:169-175
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    References listed on IDEAS

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    1. Gerber, Michael U. & Kobler, Daniel, 2000. "Algorithmic approach to the satisfactory graph partitioning problem," European Journal of Operational Research, Elsevier, vol. 125(2), pages 283-291, September.
    2. Bazgan, Cristina & Tuza, Zsolt & Vanderpooten, Daniel, 2010. "Satisfactory graph partition, variants, and generalizations," European Journal of Operational Research, Elsevier, vol. 206(2), pages 271-280, October.
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