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On Approximating (Connected) 2-Edge Dominating Set by a Tree

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Book cover Computer Science – Theory and Applications (CSR 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9691))

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Abstract

The edge dominating set problem (EDS) is to compute a minimum edge set such that every edge is dominated by some edge in it. This paper considers a variant of EDS with extensions of multiple and connected dominations combined. In the b-EDS problem, each edge needs to be dominated b times. Connected EDS requires an edge dominating set to be connected while it has to form a tree in Tree Cover. Although each of EDS, b-EDS, and Connected EDS (or Tree Cover) has been well studied, each known to be approximable within 2 (or 8/3 for b-EDS in general), nothing is known when these extensions are imposed simultaneously on EDS unlike in the case of the (vertex) dominating set problem.

We consider Connected 2-EDS and 2-Tree Cover (i.e., a combination of 2-EDS and Tree Cover), and present a polynomial algorithm approximating each within 2. Moreover, it will be shown that the single tree computed is no larger than twice the optimum for (not necessarily connected) 2-EDS, thus also approximating 2-EDS equally well. It also implies that 2-EDS with clustering properties can be approximated within 2 as well.

This work is supported in part by the Kayamori Foundation of Informational Science Advancement and JSPS KAKENHI under Grant Number 26330010.

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Authors and Affiliations

  1. Department of Computer Science and Engineering, Toyohashi University of Technology, Toyohashi, 441-8580, Japan

    Toshihiro Fujito & Tomoaki Shimoda

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  1. Toshihiro Fujito
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  2. Tomoaki Shimoda
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Correspondence to Toshihiro Fujito .

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Editors and Affiliations

  1. Russian Academy of Sciences, St. Petersburg, Russia

    Alexander S. Kulikov

  2. Technische Universiteit Eindhoven, Eindhoven, The Netherlands

    Gerhard J. Woeginger

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Fujito, T., Shimoda, T. (2016). On Approximating (Connected) 2-Edge Dominating Set by a Tree. In: Kulikov, A., Woeginger, G. (eds) Computer Science – Theory and Applications. CSR 2016. Lecture Notes in Computer Science(), vol 9691. Springer, Cham. https://doi.org/10.1007/978-3-319-34171-2_12

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  • DOI: https://doi.org/10.1007/978-3-319-34171-2_12

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  • Online ISBN: 978-3-319-34171-2

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