TY - GEN

T1 - Conflict-free colorings of shallow discs

AU - Alon, Noga

AU - Smorodinsky, Shakhar

N1 - Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2006

Y1 - 2006

N2 - We prove that any collection of n discs in which each one intersects at most k others, can be colored with at most O(log3 k) colors so that for each point p in the union of all discs there is at least one disc in the collection containing p whose color differs from that of all other members of the collection that contain p. This is motivated by a problem on frequency assignments in cellular networks, and improves the best previously known upper bound of O(log n) when k is much smaller than n.

AB - We prove that any collection of n discs in which each one intersects at most k others, can be colored with at most O(log3 k) colors so that for each point p in the union of all discs there is at least one disc in the collection containing p whose color differs from that of all other members of the collection that contain p. This is motivated by a problem on frequency assignments in cellular networks, and improves the best previously known upper bound of O(log n) when k is much smaller than n.

KW - Conflict-free coloring

KW - Frequency-assignment

KW - Wireless

UR - http://www.scopus.com/inward/record.url?scp=33748043312&partnerID=8YFLogxK

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U2 - 10.1145/1137856.1137864

DO - 10.1145/1137856.1137864

M3 - Conference contribution

AN - SCOPUS:33748043312

SN - 1595933409

SN - 9781595933409

T3 - Proceedings of the Annual Symposium on Computational Geometry

SP - 41

EP - 43

BT - Proceedings of the Twenty-Second Annual Symposium on Computational Geometry 2006, SCG'06

PB - Association for Computing Machinery (ACM)

T2 - 22nd Annual Symposium on Computational Geometry 2006, SCG'06

Y2 - 5 June 2006 through 7 June 2006

ER -