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.MFCS.2020.71
URN: urn:nbn:de:0030-drops-127404
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/12740/
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Morawietz, Nils ; Rehs, Carolin ; Weller, Mathias

A Timecop’s Work Is Harder Than You Think

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LIPIcs-MFCS-2020-71.pdf (0.6 MB)

Abstract

We consider the (parameterized) complexity of a cop and robber game on periodic, temporal graphs and a problem on periodic sequences to which these games relate intimately. In particular, we show that it is NP-hard to decide (a) whether there is some common index at which all given periodic, binary sequences are 0, and (b) whether a single cop can catch a single robber on an edge-periodic temporal graph. We further present results for various parameterizations of both problems and show that hardness not only applies in general, but also for highly limited instances. As one main result we show that even if the graph has a size-2 vertex cover and is acyclic in each time step, the cop and robber game on periodic, temporal graphs is NP-hard and W[1]-hard when parameterized by the size of the underlying input graph.

BibTeX - Entry

@InProceedings{morawietz_et_al:LIPIcs:2020:12740,
  author =	{Nils Morawietz and Carolin Rehs and Mathias Weller},
  title =	{{A Timecop’s Work Is Harder Than You Think}},
  booktitle =	{45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)},
  pages =	{71:1--71:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-159-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{170},
  editor =	{Javier Esparza and Daniel Kr{\'a}ľ},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/12740},
  URN =		{urn:nbn:de:0030-drops-127404},
  doi =		{10.4230/LIPIcs.MFCS.2020.71},
  annote =	{Keywords: edge-periodic temporal graphs, cops and robbers, tally-intersection, congruence satisfyability}
}

Keywords: edge-periodic temporal graphs, cops and robbers, tally-intersection, congruence satisfyability
Collection: 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)
Issue Date: 2020
Date of publication: 18.08.2020

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