Optimal cover of points by disks in a simple polygon

Haim Kaplan; Matthew J. Katz; Gila Morgenstern; Micha Sharir

doi:10.1007/978-3-642-15775-2_41

Optimal cover of points by disks in a simple polygon

Haim Kaplan^*, Matthew J. Katz, Gila Morgenstern, Micha Sharir

^*Corresponding author for this work

School of Computer Science

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

3 Scopus citations

Abstract

Let P be a simple polygon, and let Q be a set of points in P. We present an almost-linear time algorithm for computing a minimum cover of Q by disks that are contained in P. We generalize the algorithm above, so that it can compute a minimum cover of Q by homothets of any fixed compact convex set of constant description complexity that are contained in P. This improves previous results of Katz and Morgenstern [20]. We also consider the disk-cover problem when Q is contained in a (not too wide) annulus, and present a nearly linear algorithm for this case too.

Original language	English
Title of host publication	Algorithms, ESA 2010 - 18th Annual European Symposium, Proceedings
Pages	475-486
Number of pages	12
Edition	PART 1
DOIs	https://doi.org/10.1007/978-3-642-15775-2_41
State	Published - 2010
Event	18th Annual European Symposium on Algorithms, ESA 2010 - Liverpool, United Kingdom Duration: 6 Sep 2010 → 8 Sep 2010

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Number	PART 1
Volume	6346 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	18th Annual European Symposium on Algorithms, ESA 2010
Country/Territory	United Kingdom
City	Liverpool
Period	6/09/10 → 8/09/10

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10.1007/978-3-642-15775-2_41

Cite this

Kaplan, H., Katz, M. J., Morgenstern, G., & Sharir, M. (2010). Optimal cover of points by disks in a simple polygon. In Algorithms, ESA 2010 - 18th Annual European Symposium, Proceedings (PART 1 ed., pp. 475-486). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6346 LNCS, No. PART 1). https://doi.org/10.1007/978-3-642-15775-2_41

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title = "Optimal cover of points by disks in a simple polygon",

abstract = "Let P be a simple polygon, and let Q be a set of points in P. We present an almost-linear time algorithm for computing a minimum cover of Q by disks that are contained in P. We generalize the algorithm above, so that it can compute a minimum cover of Q by homothets of any fixed compact convex set of constant description complexity that are contained in P. This improves previous results of Katz and Morgenstern [20]. We also consider the disk-cover problem when Q is contained in a (not too wide) annulus, and present a nearly linear algorithm for this case too.",

author = "Haim Kaplan and Katz, {Matthew J.} and Gila Morgenstern and Micha Sharir",

year = "2010",

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Kaplan, H, Katz, MJ, Morgenstern, G & Sharir, M 2010, Optimal cover of points by disks in a simple polygon. in Algorithms, ESA 2010 - 18th Annual European Symposium, Proceedings. PART 1 edn, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), no. PART 1, vol. 6346 LNCS, pp. 475-486, 18th Annual European Symposium on Algorithms, ESA 2010, Liverpool, United Kingdom, 6/09/10. https://doi.org/10.1007/978-3-642-15775-2_41

Optimal cover of points by disks in a simple polygon. / Kaplan, Haim; Katz, Matthew J.; Morgenstern, Gila et al.
Algorithms, ESA 2010 - 18th Annual European Symposium, Proceedings. PART 1. ed. 2010. p. 475-486 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6346 LNCS, No. PART 1).

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

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Kaplan H, Katz MJ, Morgenstern G, Sharir M. Optimal cover of points by disks in a simple polygon. In Algorithms, ESA 2010 - 18th Annual European Symposium, Proceedings. PART 1 ed. 2010. p. 475-486. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); PART 1). doi: 10.1007/978-3-642-15775-2_41

Optimal cover of points by disks in a simple polygon

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