Sorting permutations by block-interchanges
Information Processing Letters
Algorithms on strings, trees, and sequences: computer science and computational biology
Algorithms on strings, trees, and sequences: computer science and computational biology
Sorting by reversals is difficult
RECOMB '97 Proceedings of the first annual international conference on Computational molecular biology
SIAM Journal on Discrete Mathematics
Sorting by bounded block-moves
Discrete Applied Mathematics - Special volume on computational molecular biology DAM-CMB series volume 2
CPM '96 Proceedings of the 7th Annual Symposium on Combinatorial Pattern Matching
Sorting and Selection with Structured Costs
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Improved bounds on sorting with length-weighted reversals
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Pattern matching with address errors: rearrangement distances
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Approximate String Matching with Address Bit Errors
CPM '08 Proceedings of the 19th annual symposium on Combinatorial Pattern Matching
On the cost of interchange rearrangement in strings
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Efficient computations of l1and l∞rearrangement distances
SPIRE'07 Proceedings of the 14th international conference on String processing and information retrieval
Sorting and selection with random costs
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
Transposition Rearrangement: Linear Algorithm for Length-Cost Model
Annales UMCS, Informatica
Transposition Rearrangement: Linear Algorithm for Length-Cost Model
Annales UMCS, Informatica
String rearrangement metrics: a survey
Algorithms and Applications
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Given an input string S and a target string T when S is a permutation of T , the interchange rearrangement problem is to apply on S a sequence of interchanges, such that S is transformed into T . The interchange operation exchanges the position of the two elements on which it is applied. The goal is to transform S into T at the minimum cost possible, referred to as the distance between S and T . The distance can be defined by several cost models that determine the cost of every operation. There are two known models: The Unit-cost model and the Length-cost model . In this paper, we suggest a natural cost model: The Element-cost model . In this model, the cost of an operation is determined by the elements that participate in it. Though this model has been studied in other fields, it has never been considered in the context of rearrangement problems. We consider both the special case where all elements in S and T are distinct, referred to as a permutation string , and the general case, referred to as a general string . An efficient optimal algorithm for the permutation string case and efficient approximation algorithms for the general string case, which is $\cal{NP}$-hard, are presented.