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DOI: 10.4230/LIPIcs.ICALP.2018.107
URN: urn:nbn:de:0030-drops-91113
URL: https://drops.dagstuhl.de/opus/volltexte/2018/9111/
Chaplick, Steven ; De, Minati ; Ravsky, Alexander ; Spoerhase, Joachim
Brief Announcement: Approximation Schemes for Geometric Coverage Problems
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Abstract
In this announcement, we show that the classical Maximum Coverage problem (MC) admits a PTAS via local search in essentially all cases where the corresponding instances of Set Cover (SC) admit a PTAS via the local search approach by Mustafa and Ray [Nabil H. Mustafa and Saurabh Ray, 2010]. As a corollary, we answer an open question by Badanidiyuru, Kleinberg, and Lee [Ashwinkumar Badanidiyuru et al., 2012] regarding half-spaces in R^3 thereby settling the existence of PTASs for essentially all natural cases of geometric MC problems. As an intermediate result, we show a color-balanced version of the classical planar subdivision theorem by Frederickson [Greg N. Frederickson, 1987]. We believe that some of our ideas may be useful for analyzing local search in other settings involving a hard cardinality constraint.
BibTeX - Entry
@InProceedings{chaplick_et_al:LIPIcs:2018:9111,
author = {Steven Chaplick and Minati De and Alexander Ravsky and Joachim Spoerhase},
title = {{Brief Announcement: Approximation Schemes for Geometric Coverage Problems}},
booktitle = {45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)},
pages = {107:1--107:4},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-076-7},
ISSN = {1868-8969},
year = {2018},
volume = {107},
editor = {Ioannis Chatzigiannakis and Christos Kaklamanis and D{\'a}niel Marx and Donald Sannella},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2018/9111},
URN = {urn:nbn:de:0030-drops-91113},
doi = {10.4230/LIPIcs.ICALP.2018.107},
annote = {Keywords: balanced separators, maximum coverage, local search, approximation scheme, geometric approximation algorithms}
}
| Keywords: | balanced separators, maximum coverage, local search, approximation scheme, geometric approximation algorithms | |
| Seminar: | 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018) | |
| Issue date: | 2018 | |
| Date of publication: | 04.07.2018 |
