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This paper presents a fast, randomized greedy algorithm to solve the Component Commonality Problem approximately. It is based on a geometric random walk, that starts from a given initial solution and accepts only better points during the walk. We use a new type of analysis, that is not based on conductance, but makes use of structural geometric properties of the problem, namely the smoothness of the...
Simulated Annealing is a very successful heuristic for various problems in combinatorial optimization. In this paper an application of Simulated Annealing to the 3-coloring problem is considered. In contrast to many good empirical results we will show for a certain class of graphs, that the expected first hitting time of a proper coloring, given an arbitrary cooling scheme, is of exponential size...
We will present an algorithm, based on SA-techniques and a sampling procedure, that colors a given random 3-colorable graph with high probability in sublinear time. This result is the first theoretical proof for the excellent experimental performance results of Simulated Annealing known from the literature when applied to graph coloring problems.
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