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Sorting of Permutations by Cost-Constrained Transpositions

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2 Author(s)
Farnoud, F. ; Dept. of Electr. & Comput. Eng., Univ. of Illinois at Urbana-Champaign, Champaign, IL, USA ; Milenkovic, O.

The problem of finding a minimum decomposition of a permutation in terms of transpositions with predetermined non-uniform and non-negative costs is addressed. Alternatively, computing the transposition distance between two permutations, where transpositions are endowed with arbitrary non-negative costs, is studied. For such cost functions, polynomial-time, constant-approximation decomposition algorithms are described. For metric-path costs, exact polynomial-time decomposition algorithms are presented. The algorithms in this paper 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 decompositions of cycles. The presented algorithms have a myriad of applications in information theory, bioinformatics, and algebra.

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Information Theory, IEEE Transactions on  (Volume:58 ,  Issue: 1 )