Improved Approximations for Guarding 1.5-Dimensional Terrains

Abstract : We present a 4-approximation algorithm for the problem of placing the fewest guards on a 1.5D terrain so that every point of the terrain is seen by at least one guard. This improves on the currently best approximation factor of 5 (see [14]). Unlike most of the previous techniques, our method is based on rounding the linear programming relaxation of the corresponding covering problem. Besides the simplicity of the analysis, which mainly relies on decomposing the constraint matrix of the LP into totally balanced matrices, our algorithm, unlike previous work, generalizes to the weighted and partial versions of the basic problem.
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Susanne Albers and Jean-Yves Marion. 26th International Symposium on Theoretical Aspects of Computer Science STACS 2009, Feb 2009, Freiburg, Germany. IBFI Schloss Dagstuhl, pp.361-372, 2009, Proceedings of the 26th Annual Symposium on the Theoretical Aspects of Computer Science
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Khaled Elbassioni, Erik Krohn, Domagoj Matijevic, Julián Mestre, Domagoj Severdija. Improved Approximations for Guarding 1.5-Dimensional Terrains. Susanne Albers and Jean-Yves Marion. 26th International Symposium on Theoretical Aspects of Computer Science STACS 2009, Feb 2009, Freiburg, Germany. IBFI Schloss Dagstuhl, pp.361-372, 2009, Proceedings of the 26th Annual Symposium on the Theoretical Aspects of Computer Science. 〈inria-00359652〉

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