The string edit distance matching problem with moves
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Sorting Strings by Reversals and by Transpositions
SIAM Journal on Discrete Mathematics
Edit Distance with Move Operations
CPM '02 Proceedings of the 13th Annual Symposium on Combinatorial Pattern Matching
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Approximating reversal distance for strings with bounded number of duplicates
Discrete Applied Mathematics
Minimum Common String Partition Parameterized
WABI '08 Proceedings of the 8th international workshop on Algorithms in Bioinformatics
The greedy algorithm for edit distance with moves
Information Processing Letters
Scaffold filling under the breakpoint distance
RECOMB-CG'10 Proceedings of the 2010 international conference on Comparative genomics
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 problem: hardness and approximations
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
Reversal distance for strings with duplicates: linear time approximation using hitting set
WAOA'06 Proceedings of the 4th international conference on Approximation and Online Algorithms
Parameterized Complexity
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
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Minimum Common String Partition (MCSP) has drawn much attention due to its application in genome rearrangement. In this paper, we investigate three variants of MCSP: MCSP c , which requires that there are at most c elements in the alphabet; d-MCSP, which requires the occurrence of each element to be bounded by d; and x-balanced MCSP, which requires the length of blocks being in range (n/k驴x,n/k+x), where n is the length of the input strings, k is the number of blocks in the optimal common partition and x is a constant integer. We show that MCSP c is NP-hard when c驴2. As for d-MCSP, we present an FPT algorithm which runs in O 驴((d!)2k ) time. As it is still unknown whether an FPT algorithm only parameterized on k exists for the general case of MCSP, we also devise an FPT algorithm for the special case x-balanced MCSP parameterized on both k and x.