Weakly cooperative guards in grids

Authors:
Michał Małafiejski;Paweł Żyliński
Affiliations:
Department of Algorithms and System Modeling, Gdańsk University of Technology, Poland;Institute of Mathematics, Gdańsk University, Poland
Venue:
ICCSA'05 Proceedings of the 2005 international conference on Computational Science and its Applications - Volume Part I
Year:
2005

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Abstract

We show that a minimum coverage of a grid of n segments has n–p3 weakly cooperative guards, where p3 is the size of the maximum P3-matching in the intersection graph of the grid. This makes the minimum weakly cooperative guards problem in grids NP-hard, as we prove that the maximum P3-matching problem in subcubic bipartite planar graphs is NP-hard. At last, we propose a 7/6-approximation algorithm for the minimum weakly cooperative guards problem.