License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.STACS.2020.11
URN: urn:nbn:de:0030-drops-118729
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/11872/
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Kobayashi, Yusuke

An FPT Algorithm for Minimum Additive Spanner Problem

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LIPIcs-STACS-2020-11.pdf (0.6 MB)

Abstract

For a positive integer t and a graph G, an additive t-spanner of G is a spanning subgraph in which the distance between every pair of vertices is at most the original distance plus t. The Minimum Additive t-Spanner Problem is to find an additive t-spanner with the minimum number of edges in a given graph, which is known to be NP-hard. Since we need to care about global properties of graphs when we deal with additive t-spanners, the Minimum Additive t-Spanner Problem is hard to handle and hence only few results are known for it. In this paper, we study the Minimum Additive t-Spanner Problem from the viewpoint of parameterized complexity. We formulate a parameterized version of the problem in which the number of removed edges is regarded as a parameter, and give a fixed-parameter algorithm for it. We also extend our result to the case with both a multiplicative approximation factor α and an additive approximation parameter β, which we call (α, β)-spanners.

BibTeX - Entry

@InProceedings{kobayashi:LIPIcs:2020:11872,
  author =	{Yusuke Kobayashi},
  title =	{{An FPT Algorithm for Minimum Additive Spanner Problem}},
  booktitle =	{37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020)},
  pages =	{11:1--11:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-140-5},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{154},
  editor =	{Christophe Paul and Markus Bl{\"a}ser},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/11872},
  URN =		{urn:nbn:de:0030-drops-118729},
  doi =		{10.4230/LIPIcs.STACS.2020.11},
  annote =	{Keywords: Graph algorithms, Fixed-parameter tractability, Graph spanner}
}

Keywords: Graph algorithms, Fixed-parameter tractability, Graph spanner
Collection: 37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020)
Issue Date: 2020
Date of publication: 04.03.2020

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