Sorting by reversals is difficult
RECOMB '97 Proceedings of the first annual international conference on Computational molecular biology
Transforming cabbage into turnip: polynomial algorithm for sorting signed permutations by reversals
Journal of the ACM (JACM)
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
On Some Tighter Inapproximability Results (Extended Abstract)
ICAL '99 Proceedings of the 26th International Colloquium on Automata, Languages and Programming
ISAAC '02 Proceedings of the 13th International Symposium on Algorithms and Computation
Edit Distance with Move Operations
CPM '02 Proceedings of the 13th Annual Symposium on Combinatorial Pattern Matching
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)
The greedy algorithm for edit distance with moves
Information Processing Letters
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
On the minimum common integer partition problem
ACM Transactions on Algorithms (TALG)
A novel greedy algorithm for the minimum common string partition problem
ISBRA'07 Proceedings of the 3rd international conference on Bioinformatics research and applications
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
Scaffold filling under the breakpoint distance
RECOMB-CG'10 Proceedings of the 2010 international conference on Comparative genomics
Filling scaffolds with gene repetitions: maximizing the number of adjacencies
CPM'11 Proceedings of the 22nd annual conference on Combinatorial pattern matching
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
On the minimum common integer partition problem
CIAC'06 Proceedings of the 6th Italian conference on Algorithms and Complexity
Inferring positional homologs with common intervals of sequences
RCG'06 Proceedings of the RECOMB 2006 international conference on Comparative Genomics
Minimum common string partition revisited
Journal of Combinatorial Optimization
WABI'07 Proceedings of the 7th international conference on Algorithms in Bioinformatics
An Improved Approximation Algorithm for Scaffold Filling to Maximize the Common Adjacencies
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
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String comparison is a fundamental problem in computer science, with applications in areas such as computational biology, text processing or compression In this paper we address the minimum common string partition problem, a string comparison problem with tight connection to the problem of sorting by reversals with duplicates, a key problem in genome rearrangement. A partition of a string A is a sequence ${\mathcal P}=(P_{1},P_{2},...P_{m})$ of strings, called the blocks, whose concatenation is equal to A Given a partition ${\mathcal P}$ of a string A and a partition ${\mathcal Q}$ of a string B, we say that the pair $\langle\mathcal{P,Q}\rangle$ is a common partition of A and B if ${\mathcal Q}$ is a permutation of ${\mathcal P}$ The minimum common string partition problem (MCSP) is to find a common partition of two strings A and B with the minimum number of blocks The restricted version of MCSP where each letter occurs at most k times in each input string, is denoted by k-MCSP. In this paper, we show that 2-MCSP (and therefore MCSP) is NP-hard and, moreover, even APX-hard We describe a 1.1037-approximation for 2-MCSP and a linear time 4-approximation algorithm for 3-MCSP We are not aware of any better approximations.