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Online Conflict-free Coloring of Regions

Beikmohammadi, Arash | 2021

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 53726 (19)
  4. University: Sharif University of Technology
  5. Department: Computer Engineering
  6. Advisor(s): Abam, Mohammad Ali
  7. Abstract:
  8. 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. The goal is to use minimum number of colors. In this thesis we study online CF-coloring for axis-parallel rectangles in the plane which rectangles are on x-axis. We present a randomized algorithm with O(〖log〗^6 n) colors. We also prove that this algorithm works with high probability
  9. Keywords:
  10. Computational Geometry ; Randomized Algorithm ; Conflict-Free-Coloring ; Algorithms Design

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