On illuminating line segments in the plane

Jurek Czyzowicz; Eduardo Rivera-Campo; Jorge Urrutia; Joseph Zaks

doi:10.1016/0012-365X(93)E0127-P

On illuminating line segments in the plane

Jurek Czyzowicz, Eduardo Rivera-Campo, Jorge Urrutia, Joseph Zaks

Department of Mathematics

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

Abstract

Let F be a family of n convex sets in the plane. A set of light sources S illuminates F if every point on the boundary of each element of F is visible from at least one element in S. We prove that if F is a family of n line segments, n ≥11, then ⌈2n/3⌉ light sources are always sufficient to illuminate F. If all the elements in F are parallel to the x or the y-axes, then F can be illuminated by at most ⌈(n+1)/2⌉ light sources.

Original language	English
Pages (from-to)	147-153
Number of pages	7
Journal	Discrete Mathematics
Volume	137
Issue number	1-3
DOIs	https://doi.org/10.1016/0012-365X(93)E0127-P
State	Published - 20 Jan 1995

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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10.1016/0012-365X(93)E0127-P

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AB - Let F be a family of n convex sets in the plane. A set of light sources S illuminates F if every point on the boundary of each element of F is visible from at least one element in S. We prove that if F is a family of n line segments, n ≥11, then ⌈2n/3⌉ light sources are always sufficient to illuminate F. If all the elements in F are parallel to the x or the y-axes, then F can be illuminated by at most ⌈(n+1)/2⌉ light sources.

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On illuminating line segments in the plane

Abstract

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