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

41 Scopus citations


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
Issue number6
StatePublished - 1 Dec 2007


  • Approximation algorithms
  • Geometric optimization
  • Guarding

ASJC Scopus subject areas

  • Computer Science (all)
  • Mathematics (all)


Dive into the research topics of 'A constant-factor approximation algorithm for optimal 1.5D terrain guarding'. Together they form a unique fingerprint.

Cite this