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Random Structures & Algorithms
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Computers and Intractability: A Guide to the Theory of NP-Completeness
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Improved Bounds for Sampling Coloring
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Improved Inapproximability Results for MaxClique, Chromatic Number and Approximate Graph Coloring
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Coupling with the stationary distribution and improved sampling for colorings and independent sets
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Randomly coloring planar graphs with fewer colors than the maximum degree
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Removing randomness in parallel computation without a processor penalty
SFCS '88 Proceedings of the 29th Annual Symposium on Foundations of Computer Science
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WINE '08 Proceedings of the 4th International Workshop on Internet and Network Economics
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SSS'10 Proceedings of the 12th international conference on Stabilization, safety, and security of distributed systems
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CIAC'10 Proceedings of the 7th international conference on Algorithms and Complexity
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We analyze a network coloring game which was first proposed byMichael Kearns and others in their experimental study of dynamicsand behavior in social networks. In each round of the game, eachplayer, as a node in a network G, uses a simple, greedy and selfishstrategy by choosing randomly one of the available colors that isdifferent from all colors played by its neighbors in the previousround. We show that the coloring game converges to its Nashequilibrium if the number of colors is at least two more than themaximum degree. Examples are given for which convergence does nothappen with one fewer color. We also show that with probability atleast 1 − Δ, the number of roundsrequired is O(log(n/Δ)).