Coloring geometric range spaces

Greg Aloupis; Jean Cardinal; Sébastien Collette; Stefan Langerman; Shakhar Smorodinsky

doi:10.1007/978-3-540-78773-0_13

Coloring geometric range spaces

Greg Aloupis, Jean Cardinal, Sébastien Collette, Stefan Langerman, Shakhar Smorodinsky

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

7 Scopus citations

Abstract

Given a set of points in or , we aim to color them such that every region of a certain family (for instance disks) containing at least a certain number of points contains points of many different colors. Using k colors, it is not always possible to ensure that every region containing k points contains all k colors. Thus, we introduce two relaxations: either we allow the number of colors to increase to c(k), or we require that the number of points in each region increases to p(k). We give upper bounds on c(k) and p(k) for halfspaces, disks, and pseudo-disks. We also consider the dual question, where we want to color regions instead of points. This is related to previous results of Pach, Tardos and Tóth on decompositions of coverings.

Original language	English
Title of host publication	LATIN 2008
Subtitle of host publication	Theoretical Informatics - 8th Latin American Symposium, Proceedings
Pages	146-157
Number of pages	12
DOIs	https://doi.org/10.1007/978-3-540-78773-0_13
State	Published - 12 May 2008
Externally published	Yes
Event	8th Latin American TheoreticalINformatics Symposium, LATIN 2008 - Buzios, Brazil Duration: 7 Apr 2008 → 11 Apr 2008

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	4957 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	8th Latin American TheoreticalINformatics Symposium, LATIN 2008
Country/Territory	Brazil
City	Buzios
Period	7/04/08 → 11/04/08

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/978-3-540-78773-0_13

Cite this

Aloupis, G., Cardinal, J., Collette, S., Langerman, S., & Smorodinsky, S. (2008). Coloring geometric range spaces. In LATIN 2008: Theoretical Informatics - 8th Latin American Symposium, Proceedings (pp. 146-157). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4957 LNCS). https://doi.org/10.1007/978-3-540-78773-0_13

@inproceedings{5f0ec0c0e84c45e3b95cb31b37f4d655,

title = "Coloring geometric range spaces",

abstract = "Given a set of points in or , we aim to color them such that every region of a certain family (for instance disks) containing at least a certain number of points contains points of many different colors. Using k colors, it is not always possible to ensure that every region containing k points contains all k colors. Thus, we introduce two relaxations: either we allow the number of colors to increase to c(k), or we require that the number of points in each region increases to p(k). We give upper bounds on c(k) and p(k) for halfspaces, disks, and pseudo-disks. We also consider the dual question, where we want to color regions instead of points. This is related to previous results of Pach, Tardos and T{\'o}th on decompositions of coverings.",

author = "Greg Aloupis and Jean Cardinal and S{\'e}bastien Collette and Stefan Langerman and Shakhar Smorodinsky",

year = "2008",

month = may,

day = "12",

doi = "10.1007/978-3-540-78773-0_13",

language = "English",

isbn = "3540787720",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

pages = "146--157",

booktitle = "LATIN 2008",

note = "8th Latin American TheoreticalINformatics Symposium, LATIN 2008 ; Conference date: 07-04-2008 Through 11-04-2008",

}

Aloupis, G, Cardinal, J, Collette, S, Langerman, S & Smorodinsky, S 2008, Coloring geometric range spaces. in LATIN 2008: Theoretical Informatics - 8th Latin American Symposium, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 4957 LNCS, pp. 146-157, 8th Latin American TheoreticalINformatics Symposium, LATIN 2008, Buzios, Brazil, 7/04/08. https://doi.org/10.1007/978-3-540-78773-0_13

Coloring geometric range spaces. / Aloupis, Greg; Cardinal, Jean; Collette, Sébastien et al.
LATIN 2008: Theoretical Informatics - 8th Latin American Symposium, Proceedings. 2008. p. 146-157 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4957 LNCS).

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

TY - GEN

T1 - Coloring geometric range spaces

AU - Aloupis, Greg

AU - Cardinal, Jean

AU - Collette, Sébastien

AU - Langerman, Stefan

AU - Smorodinsky, Shakhar

PY - 2008/5/12

Y1 - 2008/5/12

N2 - Given a set of points in or , we aim to color them such that every region of a certain family (for instance disks) containing at least a certain number of points contains points of many different colors. Using k colors, it is not always possible to ensure that every region containing k points contains all k colors. Thus, we introduce two relaxations: either we allow the number of colors to increase to c(k), or we require that the number of points in each region increases to p(k). We give upper bounds on c(k) and p(k) for halfspaces, disks, and pseudo-disks. We also consider the dual question, where we want to color regions instead of points. This is related to previous results of Pach, Tardos and Tóth on decompositions of coverings.

AB - Given a set of points in or , we aim to color them such that every region of a certain family (for instance disks) containing at least a certain number of points contains points of many different colors. Using k colors, it is not always possible to ensure that every region containing k points contains all k colors. Thus, we introduce two relaxations: either we allow the number of colors to increase to c(k), or we require that the number of points in each region increases to p(k). We give upper bounds on c(k) and p(k) for halfspaces, disks, and pseudo-disks. We also consider the dual question, where we want to color regions instead of points. This is related to previous results of Pach, Tardos and Tóth on decompositions of coverings.

UR - http://www.scopus.com/inward/record.url?scp=43049122777&partnerID=8YFLogxK

U2 - 10.1007/978-3-540-78773-0_13

DO - 10.1007/978-3-540-78773-0_13

M3 - Conference contribution

AN - SCOPUS:43049122777

SN - 3540787720

SN - 9783540787723

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 146

EP - 157

BT - LATIN 2008

T2 - 8th Latin American TheoreticalINformatics Symposium, LATIN 2008

Y2 - 7 April 2008 through 11 April 2008

ER -

Coloring geometric range spaces

Abstract

Publication series

Conference

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this