Balanced line separators of unit disk graphs

Paz Carmi, Man Kwun Chiu, Matthew J. Katz, Matias Korman, Yoshio Okamoto, André Van Renssen, Marcel Roeloffzen, Taichi Shiitada, Shakhar Smorodinsky

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We prove a geometric version of the graph separator theorem for the unit disk intersection graph: for any set of n unit disks in the plane there exists a line ℓ such that ℓ intersects at most O(Formula presented) disks and each of the halfplanes determined by ℓ contains at most 2n/3 unit disks from the set, where m is the number of intersecting pairs of disks. We also show that an axis-parallel line intersecting O(Formula presented) disks exists, but each halfplane may contain up to 4n/5 disks. We give an almost tight lower bound (up to sublogarithmic factors) for our approach, and also show that no line-separator of sublinear size in n exists when we look at disks of arbitrary radii, even when m = 0. Proofs are constructive and suggest simple algorithms that run in linear time. Experimental evaluation has also been conducted, which shows that for random instances our method outperforms the method by Fox and Pach (whose separator has size O(Formula presented m)).

Original languageEnglish
Title of host publicationAlgorithms and Data Structures - 15th International Symposium, WADS 2017, Proceedings
EditorsFaith Ellen, Antonina Kolokolova, Jorg-Rudiger Sack
PublisherSpringer Verlag
Pages241-252
Number of pages12
ISBN (Print)9783319621265
DOIs
Publication statusPublished - 2017
Event15th International Symposium on Algorithms and Data Structures, WADS 2017 - St. John’s, Canada
Duration: 2017 Jul 312017 Aug 2

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10389 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other15th International Symposium on Algorithms and Data Structures, WADS 2017
CountryCanada
CitySt. John’s
Period17/7/3117/8/2

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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