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Conflict-free Coloring with Recoloring

Chahian Borujeni, Maryam | 2016

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 48763 (19)
  4. University: Sharif University of Technology
  5. Department: Computer Engineering
  6. Advisor(s): Abam, Mohammad Ali
  7. Abstract:
  8. A coloring of regions is conflict-free if for any covered point in the plane, there exist a region that cover it, with a unique color. In this thesis, we examine the problem of conflict-free coloring of regions in dynamic model, with minimum colors, and with the possibility of recoloring the optimal numbers of colored regions. That means, regions are inserted one by one on the plane, and by inserting any region, inserted regions shall be conflict-free. Dynamic model are divided into three categories: offline model, online with absolute positions model and online with relative positions model. The difference between these three categories is in the information contained in insertion of regions. For conflict-free coloring of intervals with different lengths in dynamic online with relative positions model O(log n) colors is used to improve the previous results. By adding the ability of recoloring to this model we can do that with a constant 4 color and with O(n) recolorings in the algorithm. For conflict-free coloring of axis aligned rectangles in dynamic offline model O(log3 n) colors is used, and similar results in conflictfree coloring for axis aligned cuboids, in the static model will follow. For conflict-free coloring of axis aligned rectangles in dynamic online model with the absolute positions model O(log14 n) colors and with adding recoloring O(log6 n) colors and O(n) recolorings is used in the algorithm. In conflictfree coloring of nearly equal axis aligned rectangles in dynamic online with relative absolute positions model with recoloring, the number of colors used in the algorithm can be reduced to O(log4 n) with O(n) recolorings
  9. Keywords:
  10. Dynamic Model ; Conflict-Free-Coloring ; Interval Coloring ; Axis Aligned Rectangles ; Recoloring

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