Metropolis and Symmetric Functions: A Swan Song
نویسندگان
چکیده
The class of symmetric functions is based on the OneMax function by a subsequent assigning application of a real valued function. In this work we derive a sharp boundary between those problem instances that are solvable in polynomial time by the Metropolis algorithm and those that need at least exponential time. This result is both proven theoretically and illustrated by experimental data. The classification of functions into easy and hard problem instances allows a deep insight into the problem solving power of the Metropolis algorithm and can be used in the process of selecting an optimization algorithm for a concrete problem instance.
منابع مشابه
A Markov chain on the symmetric group and Jack symmetric functions
Hanlon, P., A Markov chain on the symmetric group and Jack symmetric functions, Discrete Mathematics 99 (1992) 123-140. Diaconis and Shahshahani studied a Markov chain Wf(l) whose states are the elements of the symmetric group S,. In W,(l), you move from a permutation n to any permutation of the form a(i, j) with equal probability. In this paper we study a deformation W,(a) of this Markov chain...
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