Sorting of Permutations by Cost-Constrained Transpositions
Information Theory
2010-07-27 v1 math.IT
Abstract
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.
Cite
@article{arxiv.1007.4236,
title = {Sorting of Permutations by Cost-Constrained Transpositions},
author = {Farzad Farnoud and Olgica Milenkovic},
journal= {arXiv preprint arXiv:1007.4236},
year = {2010}
}