Approximation schemes for covering and packing

Rom Aschner, Matthew J. Katz, Gila Morgenstern, Yelena Yuditsky

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

20 Scopus citations


The local search framework for obtaining PTASs for NP-hard geometric optimization problems was introduced, independently, by Chan and Har-Peled [6] and Mustafa and Ray [17]. In this paper, we generalize the framework by extending its analysis to additional families of graphs, beyond the family of planar graphs. We then present several applications of the generalized framework, some of which are very different from those presented to date (using the original framework). These applications include PTASs for finding a maximum l-shallow set of a set of fat objects, for finding a maximum triangle matching in an l-shallow unit disk graph, and for vertex-guarding a (not-necessarily- simple) polygon under an appropriate shallowness assumption. We also present a PTAS (using the original framework) for the important problem where one has to find a minimum-cardinality subset of a given set of disks (of varying radii) that covers a given set of points, and apply it to a class cover problem (studied in [3]) to obtain an improved solution.

Original languageEnglish
Title of host publicationWALCOM
Subtitle of host publicationAlgorithms and Computation - 7th International Workshop, WALCOM 2013, Proceedings
Number of pages12
StatePublished - 4 Feb 2013
Event7th International Workshop on Algorithms and Computation, WALCOM 2013 - Kharagpur, India
Duration: 14 Feb 201316 Feb 2013

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7748 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference7th International Workshop on Algorithms and Computation, WALCOM 2013

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science (all)


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