Improved Approximations for Guarding 1.5-Dimensional Terrains

Authors Khaled Elbassioni, Erik Krohn, Domagoj Matijevic, Julian Mestre, Domagoj Severdija

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Khaled Elbassioni
Erik Krohn
Domagoj Matijevic
Julian Mestre
Domagoj Severdija

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Khaled Elbassioni, Erik Krohn, Domagoj Matijevic, Julian Mestre, and Domagoj Severdija. Improved Approximations for Guarding 1.5-Dimensional Terrains. In 26th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 3, pp. 361-372, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)


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 (J. King, 2006). 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.
  • Covering problems
  • Guarding 1.5-terrains
  • Approximation algorithms
  • Linear programming
  • Totally balanced matrices


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