Conflict-Free Coloring for Moving Objects

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Biabani, Leyla | 2019

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 52392 (19)
University: Sharif University of Technology
Department: Computer Engineering
Advisor(s): Abam, Mohammad Ali
Abstract:
Let S be a set of n regions of some fixed type (such as discs, axis-parallel rectangles, etc). A conflict-free coloring (CF-coloring) of S is an assignment of colors to each region such that for every point p covered by a non-empty subset of S, there is a region with a unique color among the regions containing p. We try to maintain a CF-coloring as the objects move. Regions are moving, so after an intersection, the coloring might not be conflict-free anymore and we need to recolor some regions. The goal is to recognize the intersections and to minimize both the total number of colors used and the number of recolorings needed. In this thesis we study kinetic CF-coloring for moving axis-parallel rectangles in the plane and also rectangles moving on x-axis. A method is presented for axis-parallel rectangles and it is showed that this method requires O(log4 n) colors and O(log n) recolorings per event. For rectangles moving on x-axis, we find two solutions: first using O(log n) colors and an amortized O(log n) recolorings per event, and second O(log2 n) colors and O(log n) recolorings
Keywords:
Conflict-Free-Coloring ; Moving Objects ; Kinetic Data Structure