License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.MFCS.2023.49
URN: urn:nbn:de:0030-drops-185837
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2023/18583/
Go to the corresponding LIPIcs Volume Portal

Gahlawat, Harmender ; Zehavi, Meirav

Parameterized Analysis of the Cops and Robber Game

pdf-format:
LIPIcs-MFCS-2023-49.pdf (0.9 MB)

Abstract

Pursuit-evasion games have been intensively studied for several decades due to their numerous applications in artificial intelligence, robot motion planning, database theory, distributed computing, and algorithmic theory. Cops and Robber (CnR) is one of the most well-known pursuit-evasion games played on graphs, where multiple cops pursue a single robber. The aim is to compute the cop number of a graph, k, which is the minimum number of cops that ensures the capture of the robber.
From the viewpoint of parameterized complexity, CnR is W[2]-hard parameterized by k [Fomin et al., TCS, 2010]. Thus, we study structural parameters of the input graph. We begin with the vertex cover number (vcn). First, we establish that k ≤ vcn/3+1. Second, we prove that CnR parameterized by vcn is FPT by designing an exponential kernel. We complement this result by showing that it is unlikely for CnR parameterized by vcn to admit a polynomial compression. We extend our exponential kernels to the parameters cluster vertex deletion number and deletion to stars number, and design a linear vertex kernel for neighborhood diversity. Additionally, we extend all of our results to several well-studied variations of CnR.

BibTeX - Entry

@InProceedings{gahlawat_et_al:LIPIcs.MFCS.2023.49,
  author =	{Gahlawat, Harmender and Zehavi, Meirav},
  title =	{{Parameterized Analysis of the Cops and Robber Game}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{49:1--49:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2023/18583},
  URN =		{urn:nbn:de:0030-drops-185837},
  doi =		{10.4230/LIPIcs.MFCS.2023.49},
  annote =	{Keywords: Cops and Robber, Kernelization, Graph Searching, Fixed parameter tractability}
}

Keywords: Cops and Robber, Kernelization, Graph Searching, Fixed parameter tractability
Collection: 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)
Issue Date: 2023
Date of publication: 21.08.2023

DROPS-Home | Fulltext Search | Imprint | Privacy Published by LZI