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

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

doi:10.1137/S0097539704446384

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

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

Department of Computer Science

Research output: Contribution to journal › Article › peer-review

47 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 language	English
Pages (from-to)	1631-1647
Number of pages	17
Journal	SIAM Journal on Computing
Volume	36
Issue number	6
DOIs	https://doi.org/10.1137/S0097539704446384
State	Published - 1 Dec 2007

Keywords

Approximation algorithms
Geometric optimization
Guarding

ASJC Scopus subject areas

General Computer Science
General Mathematics

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10.1137/S0097539704446384

Cite this

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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.",

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KW - Approximation algorithms

KW - Geometric optimization

KW - Guarding

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ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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