Sorting permutations by block-interchanges
Information Processing Letters
Polynomial-time algorithm for computing translocation distance between genomes
Discrete Applied Mathematics - Special volume on computational molecular biology
SIAM Journal on Discrete Mathematics
Transforming cabbage into turnip: polynomial algorithm for sorting signed permutations by reversals
Journal of the ACM (JACM)
Sorting Permutations by Reversals and Eulerian Cycle Decompositions
SIAM Journal on Discrete Mathematics
Improved bounds on sorting with length-weighted reversals
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Reversals and Transpositions Over Finite Alphabets
SIAM Journal on Discrete Mathematics
Pattern matching with address errors: rearrangement distances
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
A very elementary presentation of the Hannenhalli-Pevzner theory
Discrete Applied Mathematics
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Consider the following optimization problem: given two strings over the same alphabet, transform one into another by a succession of interchanges of two elements. In each interchange the two participating elements exchange positions. An interchange is given a weight that depends on the distance in the string between the two exchanged elements. The object is to minimize the total weight of the interchanges. This problem is a generalization of a classical problem on permutations (where every element appears once). The generalization considers general strings with possibly repeating elements, and a function assigning weights to the interchanges. The generalization to general strings (with unit weights) was mentioned by Cayley in the 19th century, and its complexity has been an open question since. We solve this open problem and consider various weight functions as well.