A polynomial-time approximation scheme for the geometric unique coverage problem on unit squares

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

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

8 Citations (Scopus)

Abstract

We give a polynomial-time approximation scheme for the unique unit-square coverage problem: given a set of points and a set of axis-parallel unit squares, both in the plane, we wish to find a subset of squares that maximizes the number of points contained in exactly one square in the subset. Erlebach and van Leeuwen (2008) introduced this problem as the geometric version of the unique coverage problem, and the best approximation ratio by van Leeuwen (2009) before our work was 2. Our scheme can be generalized to the budgeted unique unit-square coverage problem, in which each point has a profit, each square 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 publicationAlgorithm Theory, SWAT 2012 - 13th Scandinavian Symposium and Workshops, Proceedings
Pages24-35
Number of pages12
DOIs
Publication statusPublished - 2012
Event13th Scandinavian Symposium and Workshops on Algorithm Theory, SWAT 2012 - Helsinki, Finland
Duration: 2012 Jul 42012 Jul 6

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7357 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other13th Scandinavian Symposium and Workshops on Algorithm Theory, SWAT 2012
CountryFinland
CityHelsinki
Period12/7/412/7/6

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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