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Linear Time Algorithms for Generalized Edge Dominating Set Problems

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Algorithms and Data Structures (WADS 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3608))

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Abstract

In this paper we consider a generalization of the edge dominating set (EDS) problem, in which each edge e needs to be covered b e times and refer to this as the b-EDS problem. We present an exact linear time primal dual algorithm for the weighted b-EDS problem on trees with b e ∈ {0,1}, and our algorithm generates an optimal dual solution as well. We also present an exact linear time algorithm for the unweighted b-EDS problem on trees. For general graphs we exhibit a relationship between this problem and the maximum weight matching problem. We exploit this relationship to show that a known linear time \(\frac{1}{2}\)-approximation algorithm for the weighted matching problem is also a 2-approximation algorithm for the unweighted b-EDS problem on general graphs.

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Author information

Authors and Affiliations

  1. Department of Mathematics and Computer Science, Emory University, Atlanta, GA, 30322, USA

    André Berger & Ojas Parekh

Authors
  1. André Berger
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  2. Ojas Parekh
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Editor information

Editors and Affiliations

  1. Carleton University, Ottawa, Canada

    Frank Dehne

  2. Cheriton School of Computer Science, University of Waterloo, N2L 3G1, Waterloo, Ont., Canada

    Alejandro López-Ortiz

  3. School of Computer Science, Carleton University, 1125 Colonel By Drive, K1S 5B6, Ottawa, Canada

    Jörg-Rüdiger Sack

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© 2005 Springer-Verlag Berlin Heidelberg

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Berger, A., Parekh, O. (2005). Linear Time Algorithms for Generalized Edge Dominating Set Problems. In: Dehne, F., López-Ortiz, A., Sack, JR. (eds) Algorithms and Data Structures. WADS 2005. Lecture Notes in Computer Science, vol 3608. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11534273_21

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  • DOI: https://doi.org/10.1007/11534273_21

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-28101-6

  • Online ISBN: 978-3-540-31711-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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