Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Efficient algorithms for multichromosomal genome rearrangements
Journal of Computer and System Sciences - Computational biology 2002
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Minimum Common String Partition Parameterized
WABI '08 Proceedings of the 8th international workshop on Algorithms in Bioinformatics
The ExemplarBreakpointDistance for Non-trivial Genomes Cannot Be Approximated
WALCOM '09 Proceedings of the 3rd International Workshop on Algorithms and Computation
The greedy algorithm for edit distance with moves
Information Processing Letters
Minimum common string partition revisited
FAW'10 Proceedings of the 4th international conference on Frontiers in algorithmics
The zero exemplar distance problem
RECOMB-CG'10 Proceedings of the 2010 international conference on Comparative genomics
Scaffold filling under the breakpoint distance
RECOMB-CG'10 Proceedings of the 2010 international conference on Comparative genomics
The approximability of the exemplar breakpoint distance problem
AAIM'06 Proceedings of the Second international conference on Algorithmic Aspects in Information and Management
Minimum common string partition problem: hardness and approximations
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
Non-breaking similarity of genomes with gene repetitions
CPM'07 Proceedings of the 18th annual conference on Combinatorial Pattern Matching
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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In genome sequencing there is a trend not to complete the sequence of the whole genomes. Motivated by this Muñoz et al. recently studied the (one-sided) problem of filling an incomplete multichromosomal genome (or scaffold) H with respect to a complete target genome C such that the resulting genomic (or double-cut-and-join, DCJ for short) distance between H′ and C is minimized, where H′ is the corresponding filled scaffold. Jiang et al. recently extended this result to both the breakpoint distance and the DCJ distance and to the (two-sided) case when even C has some missing genes, and solved all these problems in polynomial time. However, when H and C contain duplicated genes, the corresponding breakpoint distance problem becomes NP-complete and there has been no efficient approximation or FPT algorithms for it. In this paper, we mainly consider the one-sided problem of filling scaffolds with gene repetitions so as to maximize the number of adjacencies between the two resulting sequences; namely, given an incomplete genome I and a complete genome G, both with gene repetitions, fill in the missing genes to obtain I′ such that the number of adjacencies between I′ and G is maximized. We prove that this problem is also NP-complete and present an efficient 1.33-approximation for the problem. The hardness result also holds for the two-sided problem for which a trivial factor-2 approximation exists. We also present FPT algorithms for some special cases of this problem.