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 -