TY - GEN

T1 - The potential to improve the choice

T2 - 27th Annual ACM Symposium on Computational Geometry, SCG'11

AU - Cheilaris, Panagiotis

AU - Smorodinsky, Shakhar

AU - Sulovský, Marek

PY - 2011/7/15

Y1 - 2011/7/15

N2 - Given a geometric hypergraph (or a range-space) H = (V; E), a coloring of its vertices is said to be conict-free if for every hyperedge S ∈ E there is at least one vertex in S whose color is distinct from the colors of all other vertices in S. The study of this notion is motivated by frequency assignment problems in wireless networks. We study the list-coloring (or choice) version of this notion. In this version, each vertex is associated with a set of (admissible) colors and it is allowed to be colored only with colors from its set. List coloring arises naturally in the context of wireless networks. Our main result is a list coloring algorithm based on anew potential method. The algorithm produces a stronger unique-maximum coloring, in which colors are positive integers and the maximum color in every hyperedge occurs uniquely. As a corollary, we provide asymptotically sharp bounds on the size of the lists required to assure the existence of such unique-maximum colorings for many geometric hypergraphs (e.g., discs or pseudo-discs in the plane or points with respect to discs). Moreover, we provide an algorithm, such that, given a family of lists with the appropriate sizes, computes such a coloring from these lists.

AB - Given a geometric hypergraph (or a range-space) H = (V; E), a coloring of its vertices is said to be conict-free if for every hyperedge S ∈ E there is at least one vertex in S whose color is distinct from the colors of all other vertices in S. The study of this notion is motivated by frequency assignment problems in wireless networks. We study the list-coloring (or choice) version of this notion. In this version, each vertex is associated with a set of (admissible) colors and it is allowed to be colored only with colors from its set. List coloring arises naturally in the context of wireless networks. Our main result is a list coloring algorithm based on anew potential method. The algorithm produces a stronger unique-maximum coloring, in which colors are positive integers and the maximum color in every hyperedge occurs uniquely. As a corollary, we provide asymptotically sharp bounds on the size of the lists required to assure the existence of such unique-maximum colorings for many geometric hypergraphs (e.g., discs or pseudo-discs in the plane or points with respect to discs). Moreover, we provide an algorithm, such that, given a family of lists with the appropriate sizes, computes such a coloring from these lists.

KW - Algorithms

KW - Theory

UR - http://www.scopus.com/inward/record.url?scp=79960152738&partnerID=8YFLogxK

U2 - 10.1145/1998196.1998266

DO - 10.1145/1998196.1998266

M3 - Conference contribution

AN - SCOPUS:79960152738

SN - 9781450306829

T3 - Proceedings of the Annual Symposium on Computational Geometry

SP - 424

EP - 432

BT - Proceedings of the 27th Annual Symposium on Computational Geometry, SCG'11

Y2 - 13 June 2011 through 15 June 2011

ER -