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Parameterized Approximation Algorithms for Some Location Problems in Graphs

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Combinatorial Optimization and Applications (COCOA 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10628))

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Abstract

We develop efficient parameterized, with additive error, approximation algorithms for the (Connected) r-Domination problem and the (Connected) p-Center problem for unweighted and undirected graphs. Given a graph G, we show how to construct a (connected) \(\big (r + \mathcal {O}(\mu ) \big )\)-dominating set D with \(|D| \le |D^*|\) efficiently. Here, \(D^*\) is a minimum (connected) r-dominating set of G and \(\mu \) is our graph parameter, which is the tree-breadth or the cluster diameter in a layering partition of G. Additionally, we show that a \(+ \mathcal {O}(\mu )\)-approximation for the (Connected) p-Center problem on G can be computed in polynomial time. Our interest in these parameters stems from the fact that in many real-world networks, including Internet application networks, web networks, collaboration networks, social networks, biological networks, and others, and in many structured classes of graphs these parameters are small constants.

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Author information

Authors and Affiliations

  1. Department of Computer Science, Central Washington University, Ellensburg, WA, USA

    Arne Leitert

  2. Department of Computer Science, Kent State University, Kent, OH, USA

    Feodor F. Dragan

Authors
  1. Arne Leitert
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  2. Feodor F. Dragan
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Correspondence to Arne Leitert .

Editor information

Editors and Affiliations

  1. Shanghai Jiao Tong University, Shanghai, China

    Xiaofeng Gao

  2. Harbin Institute of Technology, Shenzhen, China

    Hongwei Du

  3. Kennesaw State University, Kennesaw, Georgia, USA

    Meng Han

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Leitert, A., Dragan, F.F. (2017). Parameterized Approximation Algorithms for Some Location Problems in Graphs. In: Gao, X., Du, H., Han, M. (eds) Combinatorial Optimization and Applications. COCOA 2017. Lecture Notes in Computer Science(), vol 10628. Springer, Cham. https://doi.org/10.1007/978-3-319-71147-8_24

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  • DOI: https://doi.org/10.1007/978-3-319-71147-8_24

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  • Publisher Name: Springer, Cham

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  • Online ISBN: 978-3-319-71147-8

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