Sorting of Permutations by Cost-Constrained Transpositions

Details Sorting of Permutations by Cost-Constrained Transpositions Sorting of Permutations by Cost-Constrained Transpositions

2010-07-24

arxiv.org/abs/1007.4236v1

Computer Science

Information Theory

Scientific paper

We address the problem of finding the minimum decomposition of a permutation in terms of transpositions with non-uniform cost. For arbitrary non-negative cost functions, we describe polynomial-time, constant-approximation decomposition algorithms. For metric-path costs, we describe exact polynomial-time decomposition algorithms. Our algorithms represent a combination of Viterbi-type algorithms and graph-search techniques for minimizing the cost of individual transpositions, and dynamic programing algorithms for finding minimum cost cycle decompositions. The presented algorithms have applications in information theory, bioinformatics, and algebra.

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