Brief Announcement - Approximation Schemes for Geometric Coverage Problems

Steven Chaplick; Minati De; Alexander Ravsky; Joachim Spoerhase

doi:10.4230/LIPICS.ICALP.2018.107

Brief Announcement - Approximation Schemes for Geometric Coverage Problems

Steven Chaplick, Minati De, Alexander Ravsky, Joachim Spoerhase

Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceeding › Academic › peer-review

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 [7]. As a corollary, we answer an open question by Badanidiyuru, Kleinberg, and Lee [1] regarding half-spaces in R³ 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 [5]. We believe that some of our ideas may be useful for analyzing local search in other settings involving a hard cardinality constraint.

Original language	English
Title of host publication	45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)
Editors	Ioannis Chatzigiannakis, Christos Kaklamanis, Daniel Marx, Donald Sannella
Place of Publication	Dagstuhl, Germany
Publisher	Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik
Pages	107:1-107:4
Volume	107
ISBN (Print)	978-3-95977-076-7
DOIs	https://doi.org/10.4230/LIPICS.ICALP.2018.107
Publication status	Published - 2018
Externally published	Yes

Publication series

Series	Leibniz International Proceedings in Informatics (LIPIcs)
Volume	107
ISSN	1868-8969

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10.4230/LIPICS.ICALP.2018.107

1 Conference article in proceeding
1 Preprint

Approximation Schemes for Geometric Coverage Problems
Chaplick, S., De, M., Ravsky, A. & Spoerhase, J., 2018, 26th Annual European Symposium on Algorithms (ESA 2018). Azar, Y., Bast, H. & Herman, G. (eds.). Dagstuhl, Germany: Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, Vol. 112. p. 17:1-17:15 (Leibniz International Proceedings in Informatics (LIPIcs), Vol. 112).
Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceeding › Academic › peer-review
Approximation Schemes for Geometric Coverage Problems
Chaplick, S., De, M., Ravsky, A. & Spoerhase, J., 2016, 16 p.
Research output: Working paper / Preprint › Preprint

Open Access

Cite this

Chaplick, S., De, M., Ravsky, A., & Spoerhase, J. (2018). Brief Announcement - Approximation Schemes for Geometric Coverage Problems. In I. Chatzigiannakis, C. Kaklamanis, D. Marx, & D. Sannella (Eds.), 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018) (Vol. 107, pp. 107:1-107:4). Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik. https://doi.org/10.4230/LIPICS.ICALP.2018.107

Chaplick, Steven ; De, Minati ; Ravsky, Alexander et al. / Brief Announcement - Approximation Schemes for Geometric Coverage Problems. 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). editor / Ioannis Chatzigiannakis ; Christos Kaklamanis ; Daniel Marx ; Donald Sannella. Vol. 107 Dagstuhl, Germany : Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, 2018. pp. 107:1-107:4 (Leibniz International Proceedings in Informatics (LIPIcs), Vol. 107).

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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 [7]. As a corollary, we answer an open question by Badanidiyuru, Kleinberg, and Lee [1] regarding half-spaces in R3 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 [5]. We believe that some of our ideas may be useful for analyzing local search in other settings involving a hard cardinality constraint.",

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Chaplick, S, De, M, Ravsky, A & Spoerhase, J 2018, Brief Announcement - Approximation Schemes for Geometric Coverage Problems. in I Chatzigiannakis, C Kaklamanis, D Marx & D Sannella (eds), 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). vol. 107, Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, Dagstuhl, Germany, Leibniz International Proceedings in Informatics (LIPIcs), vol. 107, pp. 107:1-107:4. https://doi.org/10.4230/LIPICS.ICALP.2018.107

Brief Announcement - Approximation Schemes for Geometric Coverage Problems. / Chaplick, Steven; De, Minati; Ravsky, Alexander et al.
45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). ed. / Ioannis Chatzigiannakis; Christos Kaklamanis; Daniel Marx; Donald Sannella. Vol. 107 Dagstuhl, Germany: Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, 2018. p. 107:1-107:4 (Leibniz International Proceedings in Informatics (LIPIcs), Vol. 107).

Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceeding › Academic › peer-review

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AU - Chaplick, Steven

AU - De, Minati

AU - Ravsky, Alexander

AU - Spoerhase, Joachim

N1 - DBLP's bibliographic metadata records provided through http://dblp.org/search/publ/api are distributed under a Creative Commons CC0 1.0 Universal Public Domain Dedication. Although the bibliographic metadata records are provided consistent with CC0 1.0 Dedication, the content described by the metadata records is not. Content may be subject to copyright, rights of privacy, rights of publicity and other restrictions.

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Y1 - 2018

N2 - 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 [7]. As a corollary, we answer an open question by Badanidiyuru, Kleinberg, and Lee [1] regarding half-spaces in R3 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 [5]. We believe that some of our ideas may be useful for analyzing local search in other settings involving a hard cardinality constraint.

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SN - 978-3-95977-076-7

VL - 107

T3 - Leibniz International Proceedings in Informatics (LIPIcs)

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A2 - Chatzigiannakis, Ioannis

A2 - Kaklamanis, Christos

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A2 - Sannella, Donald

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ER -

Chaplick S, De M, Ravsky A, Spoerhase J. Brief Announcement - Approximation Schemes for Geometric Coverage Problems. In Chatzigiannakis I, Kaklamanis C, Marx D, Sannella D, editors, 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Vol. 107. Dagstuhl, Germany: Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik. 2018. p. 107:1-107:4. (Leibniz International Proceedings in Informatics (LIPIcs), Vol. 107). doi: 10.4230/LIPICS.ICALP.2018.107

Brief Announcement - Approximation Schemes for Geometric Coverage Problems

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Approximation Schemes for Geometric Coverage Problems

Approximation Schemes for Geometric Coverage Problems

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