A constant-factor approximation algorithm for optimal 1.5D terrain guarding

Boaz Ben-Moshe, Matthew J. Katz, Joseph S.B. Mitchell

Research output: Contribution to journalArticlepeer-review

39 Scopus citations

Abstract

We present the first constant-factor approximation algorithm for a nontrivial instance of the optimal guarding (coverage) problem in polygons. In particular, we give an O(1)-approximation algorithm for placing the fewest point guards on a 1.5D terrain, so that every point of the terrain is seen by at least one guard. While polylogarithmic-factor approximations follow from set cover results, our new results exploit the geometrie structure of terrains to obtain a substantially improved approximation algorithm.

Original languageEnglish
Pages (from-to)1631-1647
Number of pages17
JournalSIAM Journal on Computing
Volume36
Issue number6
DOIs
StatePublished - 1 Dec 2007

Keywords

  • Approximation algorithms
  • Geometric optimization
  • Guarding

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