Scaffold Filling under the Breakpoint Distance

Jiang, Haitao; Zheng, Chunfang; Sankoff, David; Zhu, Binhai

doi:10.1007/978-3-642-16181-0_8

“…Therefore, the breakpoint distance between A and B is defined as the number of breakpoints in A, which is equal to that of B. In [16] Jiang et al introduced a new related variant of the combinatorial problem, called Two-sided scaffold filling problem, where both genomes are incomplete. The authors show that when the input genomes do not contain gene repetitions the problem is polynomially solvable under both the DCJ distance and the breakpoint distance.…”

Section: A Preliminary Version Of This Paper Appeared In the Proceedimentioning

confidence: 99%

Fixed-Parameter Algorithms for Scaffold Filling

Bulteau¹,

Carrieri²,

Dondi³

2014

Lecture Notes in Computer Science

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The new sequencing technologies, called next-generation sequencing, provide a huge amount of data that can be used to reconstruct genomes. However, the methods applied to reconstruct genomes often are not able to reconstruct a complete genome and provide only an incomplete information. Here we consider two combinatorial problems that aim to reconstruct complete genomes by inserting a collection of missing genes. The first problem we consider, called One-sided scaffold filling, given an incomplete genome B and a complete genome A, asks for the insertion of missing genes into an incomplete genome B with the goal of maximizing the common adjacencies between genomes B (resulting from the insertion of missing genes in B) and A. The second problem, called Two-sided scaffold filling, given two incomplete genomes A, B, asks for the insertion of missing genes into both genomes so that the resulting genomes A and B have the same multiset of genes and the number of common adjacencies between A and B is maximized. Both problems were proved to be NP-hard, while their parameterized complexity, when the parameter is the number of common adjacencies of the resulting genomes, was left as an open problem. In this paper, we settle this open problem by presenting fixed-parameter algorithms for One-sided scaffold filling and Two-sided scaffold filling.

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“…Given two related sequences A and B, two consecutive elements a i and a i+1 in A form an adjacency if they are also consecutive in B independently from the order (i.e., as a i a i+1 or a i+1 a i ), otherwise they form a breakpoint. Therefore, the breakpoint distance between A and B is defined as the number of breakpoints in A, which is equal to that of B. Jiang et al [16] introduced a new related variant of the combinatorial problem, called Two-sided scaffold filling problem, where both genomes are incomplete. The authors show that when the input genomes do not contain gene repetitions the problem is polynomially solvable under both the DCJ distance and the breakpoint distance.…”

Section: Introductionmentioning

confidence: 99%

“…Later in [16], the scaffold filling problem has been investigated considering both the DCJ distance and the breakpoint distance. Given two related sequences A and B, two consecutive elements a i and a i+1 in A form an adjacency if they are also consecutive in B independently from the order (i.e., as a i a i+1 or a i+1 a i ), otherwise they form a breakpoint.…”

Section: Introductionmentioning

confidence: 99%

Fixed-parameter algorithms for scaffold filling

Bulteau

¹

,

Carrieri

²

,

Dondi

³

2015

Theoretical Computer Science

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The new sequencing technologies, called next-generation sequencing, provide a huge amount of data that can be used to reconstruct genomes. However, the methods applied to reconstruct genomes often are not able to reconstruct a complete genome and provide only an incomplete information. Here we consider two combinatorial problems that aim to reconstruct complete genomes by inserting a collection of missing genes. The first problem we consider, called One-sided scaffold filling, given an incomplete genome B and a complete genome A, asks for the insertion of missing genes into an incomplete genome B with the goal of maximizing the common adjacencies between genomes B (resulting from the insertion of missing genes in B) and A. The second problem, called Two-sided scaffold filling, given two incomplete genomes A, B, asks for the insertion of missing genes into both genomes so that the resulting genomes A and B have the same multiset of genes and the number of common adjacencies between A and B is maximized. Both problems were proved to be NP-hard, while their parameterized complexity, when the parameter is the number of common adjacencies of the resulting genomes, was left as an open problem. In this paper, we settle this open problem by presenting fixed-parameter algorithms for One-sided scaffold filling and Two-sided scaffold filling.

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“…In fact this problem is also connected to computing the breakpoint distance between genomes with gene duplications, which is also NP-complete and the existence of an FPT algorithm is also unknown (Jiang et al 2010). In this paper, we try to handle variants of MCSP by using additional parameters.…”

Section: Minimum Common String Partitionmentioning

confidence: 99%

Minimum common string partition revisited

Jiang

¹

,

Zhu

²

,

Zhu

³

et al. 2010

Self Cite

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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 −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 ≥ 2. As for d-MCSP, we present an FPT algorithm which runs in O * ((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.

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Scaffold Filling under the Breakpoint Distance

Cited by 15 publications

References 13 publications

Fixed-Parameter Algorithms for Scaffold Filling

Fixed-Parameter Algorithms for Scaffold Filling

Fixed-parameter algorithms for scaffold filling

Minimum common string partition revisited

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