A 4.31-approximation for the geometric unique coverage problem on unit disks

Takehiro Ito, Shin Ichi Nakano, Yoshio Okamoto, Yota Otachi, Ryuhei Uehara, Takeaki Uno, Yushi Uno

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

2 Citations (Scopus)

Abstract

We give an improved approximation algorithm for the unique unit-disk coverage problem: Given a set of points and a set of unit disks, both in the plane, we wish to find a subset of disks that maximizes the number of points contained in exactly one disk in the subset. Erlebach and van Leeuwen (2008) introduced this problem as the geometric version of the unique coverage problem, and gave a polynomial-time 18-approximation algorithm. In this paper, we improve this approximation ratio 18 to 2 + 4/√3 + ε (< 4.3095 + ε) for any fixed constant ε > 0. Our algorithm runs in polynomial time which depends exponentially on 1/ε. The algorithm can be generalized to the budgeted unique unit-disk coverage problem in which each point has a profit, each disk has a cost, and we wish to maximize the total profit of the uniquely covered points under the condition that the total cost is at most a given bound.

Original languageEnglish
Title of host publicationAlgorithms and Computation - 23rd International Symposium, ISAAC 2012, Proceedings
PublisherSpringer Verlag
Pages372-381
Number of pages10
ISBN (Print)9783642352607
DOIs
Publication statusPublished - 2012
Event23rd International Symposium on Algorithms and Computation, ISAAC 2012 - Taipei, Taiwan, Province of China
Duration: 2012 Dec 192012 Dec 21

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7676 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other23rd International Symposium on Algorithms and Computation, ISAAC 2012
Country/TerritoryTaiwan, Province of China
CityTaipei
Period12/12/1912/12/21

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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