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On Approximability of the Independent/Connected Edge Dominating Set Problems

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FST TCS 2000: Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1974))

Abstract

We investigate polynomial-time approximability of the problems related to edge dominating sets of graphs. When edges are unitweighted, the edge dominating set problem is polynomially equivalent to the minimum maximal matching problem, in either exact or approximate computation, and the former problem was recently found to be approximable within a factor of 2 even with arbitrary weights. It will be shown, in contrast with this, that the minimum weight maximal matching problem cannot be approximated within any polynomially computable factor unless P=NP.

The connected edge dominating set problem and the connected vertex cover problem also have the same approximability when edges/vertices are unit-weighted, and the former problem is known to be approximable, even with general edge weights, within a factor of 3.55. We will show that, when general weights are allowed, 1) the connected edge dominating set problem can be approximated within a factor of 3 + ∈, and 2) the connected vertex cover problem is approximable within a factor of ln n + 3 but cannot be within (1 - ∈) lnn for any ∈ > 0 unless NP ⊂ DTIME(nO(log log n)).

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Authors and Affiliations

  1. Department of Electronics, Nagoya UniversityFuro, 464-8603, Chikusa, Nagoya, Japan

    Toshihiro Fujito

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  1. Toshihiro Fujito
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Editors and Affiliations

  1. Department of Computer Science and Engineering, Indian Institute of Technology, Delhi, Hauz Khas, 110016, New Delhi, India

    Sanjiv Kapoor  & Sanjiva Prasad  & 

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Fujito, T. (2000). On Approximability of the Independent/Connected Edge Dominating Set Problems. In: Kapoor, S., Prasad, S. (eds) FST TCS 2000: Foundations of Software Technology and Theoretical Computer Science. FSTTCS 2000. Lecture Notes in Computer Science, vol 1974. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44450-5_9

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  • DOI: https://doi.org/10.1007/3-540-44450-5_9

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41413-1

  • Online ISBN: 978-3-540-44450-3

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