On neighbors in geometric permutations

Micha Sharir, Shakhar Smorodinsky

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

Abstract

We introduce a new notion of ‘neighbors’ in geometric permutations. We conjecture that the maximum number of neighbors in a set S of n pairwise disjoint convex bodies in ℝd is O(n), and we prove this conjecture for d = 2. We show that if the set of pairs of neighbors in a set S is of size N, then S admits at most O(Nd−1) geometric permutations. Hence we obtain an alternative proof of a linear upper bound on the number of geometric permutations for any finite family of pairwise disjoint convex bodies in the plane.

Original languageEnglish
Title of host publicationAlgorithm Theory - SWAT 2002 - 8th Scandinavian Workshop on Algorithm Theory, Proceedings
EditorsMartti Penttonen, Erik Meineche Schmidt
PublisherSpringer Verlag
Pages131-139
Number of pages9
ISBN (Print)9783540438663
DOIs
StatePublished - 2002
Event8th Scandinavian Workshop on Algorithm Theory, SWAT 2002 - Turku, Finland
Duration: 3 Jul 20025 Jul 2002

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume2368
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference8th Scandinavian Workshop on Algorithm Theory, SWAT 2002
Country/TerritoryFinland
CityTurku
Period3/07/025/07/02

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