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The Approximability Behaviour of Some Combinatorial Problems with Respect to the Approximability of a Class of Maximum Independent Set Problems

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Abstract

We prove that the existence of a polynomial timeρ-approximation algorithm (whereρ < 1 is a fixed constant)for a class of independent set problems, leads to a polynomial timeapproximation algorithm with approximation ratio strictly smallerthan 2 for vertex covering, while the non-existence of such analgorithm induces a lower bound on the ratio of every polynomialtime approximation algorithm for vertex covering. We also prove asimilar result for a (maximization) convex programming problemincluding quadratic programming as subproblem.

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Authors and Affiliations

  1. LAMSADE, Université Paris-Dauphine, Place du Maréchal De Lattre de Tassigny, Paris Cedex 16, France

    Marc Demange & Vangelis Th. Paschos

Authors
  1. Marc Demange
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  2. Vangelis Th. Paschos
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Demange, M., Paschos, V.T. The Approximability Behaviour of Some Combinatorial Problems with Respect to the Approximability of a Class of Maximum Independent Set Problems. Computational Optimization and Applications 7, 307–324 (1997). https://doi.org/10.1023/A:1008660812834

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  • DOI: https://doi.org/10.1023/A:1008660812834

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