Arrangements of segments that share endpoints: Single face results

E. M. Arkin*, D. Halperin, K. Kedem, J. S.B. Mitchell, N. Naor

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-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 O(h log 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(h 2). Our results show that, in a sense, 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.

Original languageEnglish
Pages (from-to)257-270
Number of pages14
JournalDiscrete and Computational Geometry
Volume13
Issue number1
DOIs
StatePublished - Dec 1995
Externally publishedYes

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