Arrangements of segments that share endpoints: Single face results

Esther M. Arkin, Dan Halperin, Klara Kedem, Joseph S.B. Mitchell, Nir Naor

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

We provide new combinatorial bounds on the complexity of a face in an arrangement of segments in the plane. In particular, we show that the complexity of a single face in an arrangement of n line segments determined by h endpoints is ⊙(ha(h)). While the previous upper bound, O(nα(n)), is tight for segments with distinct endpoints, it is far from being optimal when n = Ω(h2). Our result shows that the fundamental combinatorial complexity of a face arises not as a result of the number of segments, but rather as a result of the number of endpoints. We generalize our bounds to the case of pseudosegments, and to the case of n chords in a polygon with h holes. Furthermore, our results lead to an improved algorithm for computing a single face in an arrangement of segments that share endpoints.

Original languageEnglish
Title of host publicationProceedings of the Annual Symposium on Computational Geometry
PublisherAssociation for Computing Machinery
Pages324-333
Number of pages10
ISBN (Print)0897914260
DOIs
StatePublished - 1 Jun 1991
Externally publishedYes
Event7th Annual Symposium on Computational Geometry, SCG 1991 - North Conway, United States
Duration: 10 Jun 199112 Jun 1991

Publication series

NameProceedings of the Annual Symposium on Computational Geometry

Conference

Conference7th Annual Symposium on Computational Geometry, SCG 1991
Country/TerritoryUnited States
CityNorth Conway
Period10/06/9112/06/91

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