Chapter

Computational Science and Its Applications – ICCSA 2005

Volume 3480 of the series Lecture Notes in Computer Science pp 647-656

Weakly Cooperative Guards in Grids

  • Michał MałafiejskiAffiliated withDepartment of Algorithms and System Modeling, Gdańsk University of Technology
  • , Paweł ŻylińskiAffiliated withInstitute of Mathematics, Gdańsk University

Abstract

We show that a minimum coverage of a grid of n segments has np 3 weakly cooperative guards, where p 3 is the size of the maximum P 3-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 P 3-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.