Approximation hardness of edge dominating set problems

Abstract

We provide the first interesting explicit lower bounds on efficient approximability for two closely related optimization problems in graphs, MINIMUM EDGE DOMINATING SET and MINIMUM MAXIMAL MATCHING. We show that it is NP-hard to approximate the solution of both problems to within any constant factor smaller than \({\frac{7}{6}}\). The result extends with negligible loss to bounded degree graphs and to everywhere dense graphs.

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Correspondence to Miroslav Chlebík.

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An extended abstract of this paper was accepted at the 14th Annual International Symposium on Algorithms and Computation, ISAAC 2003.

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Chlebík, M., Chlebíková, J. Approximation hardness of edge dominating set problems. J Comb Optim 11, 279–290 (2006). https://doi.org/10.1007/s10878-006-7908-0

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Keywords

  • Minimum edge dominating set
  • Minimum maximal matching
  • Approximation lower bound
  • Bounded degree graphs
  • Everywhere dense graphs