Simulated Annealing and Graph Colouring

Authors:
Andreas Nolte;Rainer Schrader
Affiliations:
Universität zu Köln, Weyertal 80, 50931 Köln, Germany (e-mail: a.nolte@allianz.de, rs@zpr.uni-koeln.de);Universität zu Köln, Weyertal 80, 50931 Köln, Germany (e-mail: a.nolte@allianz.de, rs@zpr.uni-koeln.de)
Venue:
Combinatorics, Probability and Computing
Year:
2001

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Abstract

Simulated annealing is a very successful heuristic for various problems in combinatorial optimization. In this paper an application of simulated annealing to the 3-colouring 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 colouring, given an arbitrary cooling scheme, is of exponential size.These results are complementary to those in [13], where we prove the convergence of simulated annealing to an optimal solution in exponential time.