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
The string edit distance matching problem with moves
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Sorting Strings by Reversals and by Transpositions
SIAM Journal on Discrete Mathematics
Optimal suffix tree construction with large alphabets
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Assignment of Orthologous Genes via Genome Rearrangement
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
The greedy algorithm for the minimum common string partition problem
ACM Transactions on Algorithms (TALG)
Linear pattern matching algorithms
SWAT '73 Proceedings of the 14th Annual Symposium on Switching and Automata Theory (swat 1973)
Approximating reversal distance for strings with bounded number of duplicates
MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
Minimum Common String Partition Parameterized
WABI '08 Proceedings of the 8th international workshop on Algorithms in Bioinformatics
On the approximability of comparing genomes with duplicates
WALCOM'08 Proceedings of the 2nd international conference on Algorithms and computation
Minimum common string partition revisited
FAW'10 Proceedings of the 4th international conference on Frontiers in algorithmics
Sorting by transpositions is difficult
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Exponential and polynomial time algorithms for the minimum common string partition problem
COCOA'11 Proceedings of the 5th international conference on Combinatorial optimization and applications
Minimum common string partition revisited
Journal of Combinatorial Optimization
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In the last decade there has been an ongoing interest in string comparison problems; to a large extend the interest was stimulated by genome rearrangement problems in computational biology but related problems appear in many other areas of computer science. Particular attention has been given to the problem of sorting by reversals(SBR): given two strings, A and B, find the minimum number of reversals that transform the string A into the string B (a reversalρ(i,j), ij, transforms a string A=a1...an into a string A′=a1...ai−1ajaj−1 ...aiaj+1 ...an). Primarily the problem has been studied for strings in which every symbol appears exactly once (that is, for permutations) and only recently attention has been given to the general case where duplicates of the symbols are allowed. In this paper we consider the problem k-SBR, a version of SBR in which each symbol is allowed to appear up to k times in each string, for some k≥1. The main result of the paper is a Θ(k)-approximation algorithm for k-SBR running in time O(n); compared to the previously known algorithm for k-SBR, this is an improvement by a factor of Θ(k) in the approximation ratio, and by a factor of Θ(k) in the running time. Crucial ingredients of our algorithm are the suffix tree data structure and a linear time algorithm for a special case of a disjoint set union problem.