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.
The research of the first author is supported by the Norwegian Research Council. The research of the second author is supported by the EPSRC EP/GO43434/1. The research of the third author is supported by the project “Kapodistrias” (AΠ 02839/28.07.2008) of the National and Kapodistrian University of Athens.
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Fomin, F.V., Golovach, P.A., Thilikos, D.M. (2011). Approximation Algorithms for Domination Search. In: Jansen, K., Solis-Oba, R. (eds) Approximation and Online Algorithms. WAOA 2010. Lecture Notes in Computer Science, vol 6534. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18318-8_12
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