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.ICALP.2019.109
URN: urn:nbn:de:0030-drops-106858
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/10685/
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Casel, Katrin ; Day, Joel D. ; Fleischmann, Pamela ; Kociumaka, Tomasz ; Manea, Florin ; Schmid, Markus L.

Graph and String Parameters: Connections Between Pathwidth, Cutwidth and the Locality Number

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LIPIcs-ICALP-2019-109.pdf (0.6 MB)

Abstract

We investigate the locality number, a recently introduced structural parameter for strings (with applications in pattern matching with variables), and its connection to two important graph-parameters, cutwidth and pathwidth. These connections allow us to show that computing the locality number is NP-hard but fixed-parameter tractable (when the locality number or the alphabet size is treated as a parameter), and can be approximated with ratio O(sqrt{log{opt}} log n). As a by-product, we also relate cutwidth via the locality number to pathwidth, which is of independent interest, since it improves the best currently known approximation algorithm for cutwidth. In addition to these main results, we also consider the possibility of greedy-based approximation algorithms for the locality number.

BibTeX - Entry

@InProceedings{casel_et_al:LIPIcs:2019:10685,
  author =	{Katrin Casel and Joel D. Day and Pamela Fleischmann and Tomasz Kociumaka and Florin Manea and Markus L. Schmid},
  title =	{{Graph and String Parameters: Connections Between Pathwidth, Cutwidth and the Locality Number}},
  booktitle =	{46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)},
  pages =	{109:1--109:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-109-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{132},
  editor =	{Christel Baier and Ioannis Chatzigiannakis and Paola Flocchini and Stefano Leonardi},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2019/10685},
  URN =		{urn:nbn:de:0030-drops-106858},
  doi =		{10.4230/LIPIcs.ICALP.2019.109},
  annote =	{Keywords: Graph and String Parameters, NP-Completeness, Approximation Algorithms}
}

Keywords: Graph and String Parameters, NP-Completeness, Approximation Algorithms
Collection: 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)
Issue Date: 2019
Date of publication: 04.07.2019

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