Conflict-Free Coloring for Rectangle Ranges Using O(n.382) Colors

Ajwani, Deepak and Elbassioni, Khaled and Govindarajan, Sathish and Ray, Saurabh (2012) Conflict-Free Coloring for Rectangle Ranges Using O(n.382) Colors. In: Discrete & Computational Geometry, 48 (1). pp. 39-52.

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Abstract

Given a set of points P ⊆ R2, a conflict-free coloring of P w.r.t. rectangle ranges is an assignment of colors to points of P, such that each nonempty axisparallel rectangle T in the plane contains a point whose color is distinct from all other points in P ∩ T . This notion has been the subject of recent interest and is motivated by frequency assignment in wireless cellular networks: one naturally would like to minimize the number of frequencies (colors) assigned to base stations (points) such that within any range (for instance, rectangle), there is no interference. We show that any set of n points in R2 can be conflict-free colored with O(nβ∗+o(1)) colors in expected polynomial time, where β∗ = 3−√5 2 < 0.382.

Item Type:	Journal Article
Publication:	Discrete & Computational Geometry
Publisher:	Springer
Additional Information:	Copyright of this article is belongs to Springer.
Keywords:	Frequency assignment in wireless networks;Conflict-free coloring;Axis-parallel rectangles;Boundary sets;Monotone sequences
Department/Centre:	Division of Electrical Sciences > Computer Science & Automation
Date Deposited:	21 Jul 2012 09:12
Last Modified:	23 Jul 2012 10:11
URI:	http://eprints.iisc.ac.in/id/eprint/44850

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