Online Conflict-free Coloring Of Intervals

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Rezaei Seraji, Mohammad Javad | 2013

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 45014 (19)
University: Sharif University of Technology
Department: Computer Engineering
Advisor(s): Abam, Mohammad Ali
Abstract:
In this thesis, we consider the problem of online conflict-free coloring for regions. First, we analyze online variant of the conflict-free coloring of intervals on the line, where each newly inserted interval must be assigned a color upon insertion such that the coloring remains conflict-free, i.e. for every point p in the union of the current intervals, there must be an interval I with a unique color among all intervals covering p. we present deterministic algorithm for achieving this goal which uses O(log^3⁡n) color. Next, we consider the online conflict-free coloring of nearly-equal axis-parallel rectangles in the plane and present a deterministic algorithms which uses O(log^12⁡n) colors. This is the first efficient (i.e, using polylog(n) colors) deterministic online conflict-free coloring for this problem
Keywords:
Conflict-Free-Coloring ; Online Model ; Interval Coloring ; Nearly-Equal Axis Parallel Rectangles

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