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International Conference on Algorithms and Complexity

CIAC 2017: Algorithms and Complexity pp 234–246Cite as

Approximating Bounded Degree Deletion via Matroid Matching

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10236))

Abstract

The Bounded Degree Deletion problem with degree bound \(b: V\rightarrow \mathbb {Z}_+\) (denoted b -BDD), is that of computing a minimum cost vertex set in a graph \(G=(V, E)\) such that, when it is removed from G, the degree of any remaining vertex v is no larger than b(v). It will be shown that b-BDD can be approximated within \(\max \{2,\bar{b}/2+1\}\), improving the previous best bound for \(2\le \bar{b}\le 5\), where \(\bar{b}\) is the maximum degree bound, i.e., \(\bar{b}=\max \{b(v)\mid v\in V\}\). The new bound is attained by casting b-BDD as the vertex deletion problem for such a property inducing a 2-polymatroid on the edge set of a graph, and then reducing it to the submodular set cover problem.

T. Fujito— Supported in part by 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

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  1. Toshihiro Fujito
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Correspondence to Toshihiro Fujito .

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Editors and Affiliations

  1. National Technical University of Athens, Zografou, Athens, Greece

    Dimitris Fotakis

  2. National Technical University of Athens, Zografou, Athens, Greece

    Aris Pagourtzis

  3. Université Paris-Dauphine, Paris, France

    Vangelis Th. Paschos

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Fujito, T. (2017). Approximating Bounded Degree Deletion via Matroid Matching. In: Fotakis, D., Pagourtzis, A., Paschos, V. (eds) Algorithms and Complexity. CIAC 2017. Lecture Notes in Computer Science(), vol 10236. Springer, Cham. https://doi.org/10.1007/978-3-319-57586-5_20

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  • DOI: https://doi.org/10.1007/978-3-319-57586-5_20

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  • Online ISBN: 978-3-319-57586-5

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