Approximation algorithms for domination search

  • Authors:

  • Fedor V. Fomin;Petr A. Golovach;Dimitrios M. Thilikos

  • Affiliations:

  • Department of Informatics, University of Bergen, Bergen, Norway;School of Engineering and Computing Sciences, Durham University, Durham, UK;Department of Mathematics, University of Athens, Panepistimioupolis, Athens, Greece

  • Venue:
  • WAOA'10 Proceedings of the 8th international conference on Approximation and online algorithms
  • Year:
  • 2010

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Abstract

The r-domination search game on graphs is a game-theoretical approach to the investigation of several graph and hypergraph parameters including treewidth and hypertree width. The task is to identify the minimum number of cops sufficient to catch the visible and fast robber. In r-domination search, the robber is being arrested if he resides inside a ball of radius r around some cop. In this setting, the power of the cops does not depend only on how many they are but also on the local topology of the graph around them. This is the main reason why the approximation complexity of the r-domination search game varies considerably, depending on whether r = 0 or r ≥ 1. We prove that this discrepancy is canceled when the game is played in (non-trivial) graph classes that are closed under taking of minors. We give a constant factor approximation algorithm that for every fixed r and graph H, computes the minimum number of cops required to capture the robber in the r-domination game on graphs excluding H as a minor.