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- Type of Document: M.Sc. Thesis
- Language: Farsi
- Document No: 55555 (19)
- University: Sharif University of Technology
- Department: Computer Engineering
- Advisor(s): Abam, Mohammad Ali
- Abstract:
- Conflict-free coloring problem is one of the computational geometry problems that has been studied in the last two decades. The root of this problem comes from the frequency assignment to cellular networks problem. In that research, we have a cellular network containing several regions in two-dimensional plane and we want to assign a frequency to each of the regions so that if we look at any intersection of them, there is a region with a unique color compared to other regions of that intersection. In other words, a person’s cellular phone in the range of some regions (in the intersection of them) would be able to connect to one antenna with a unique frequency and function properly. This problem is modeled by a hypergraph. But we look at this from the game theory point of view. We model the problem as a conflict-free coloring game in hypergraphs, where each node is considered as a rational agent (those regions) deciding what color to chose for itself in each round of the game. Our final goal is to solve this coloring by exploring achievable Nash Equilibrium, Price of Anarchy, Price of Stability, as well as examining the best and worst possible Nash Equilibrium. In the described game, we are looking for a set of assigned colors for the cellular network so that no regions has the desire to change their frequencies. in this research
- Keywords:
- Hypergraph ; Nash Equilibrium Point ; Conflict-Free-Coloring ; Stability Price ; Anarchy Price
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