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Exact approaches for scaffolding.

ABSTRACT: This paper presents new structural and algorithmic results around the scaffolding problem, which occurs prominently in next generation sequencing. The problem can be formalized as an optimization problem on a special graph, the "scaffold graph". We prove that the problem is polynomial if this graph is a tree by providing a dynamic programming algorithm for this case. This algorithm serves as a basis to deduce an exact algorithm for general graphs using a tree decomposition of the input. We explore other structural parameters, proving a linear-size problem kernel with respect to the size of a feedback-edge set on a restricted version of Scaffolding. Finally, we examine some parameters of scaffold graphs, which are based on real-world genomes, revealing that the feedback edge set is significantly smaller than the input size.

SUBMITTER: Weller M

PROVIDER: S-EPMC4603742 | biostudies-literature | 2015

REPOSITORIES: biostudies-literature

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Exact approaches for scaffolding.

Weller Mathias M Chateau Annie A Giroudeau Rodolphe R

BMC bioinformatics 20151002

This paper presents new structural and algorithmic results around the scaffolding problem, which occurs prominently in next generation sequencing. The problem can be formalized as an optimization problem on a special graph, the "scaffold graph". We prove that the problem is polynomial if this graph is a tree by providing a dynamic programming algorithm for this case. This algorithm serves as a basis to deduce an exact algorithm for general graphs using a tree decomposition of the input. We explo ...[more]

PMID: 26451725

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Project description:MotivationThe motif discovery problem consists of finding over-represented patterns in a collection of biosequences. It is one of the classical sequence analysis problems, but still has not been satisfactorily solved in an exact and efficient manner. This is partly due to the large number of possibilities of defining the motif search space and the notion of over-representation. Even for well-defined formalizations, the problem is frequently solved in an ad hoc manner with heuristics that do not guarantee to find the best motif.ResultsWe show how to solve the motif discovery problem (almost) exactly on a practically relevant space of IUPAC generalized string patterns, using the p-value with respect to an i.i.d. model or a Markov model as the measure of over-representation. In particular, (i) we use a highly accurate compound Poisson approximation for the null distribution of the number of motif occurrences. We show how to compute the exact clump size distribution using a recently introduced device called probabilistic arithmetic automaton (PAA). (ii) We define two p-value scores for over-representation, the first one based on the total number of motif occurrences, the second one based on the number of sequences in a collection with at least one occurrence. (iii) We describe an algorithm to discover the optimal pattern with respect to either of the scores. The method exploits monotonicity properties of the compound Poisson approximation and is by orders of magnitude faster than exhaustive enumeration of IUPAC strings (11.8 h compared with an extrapolated runtime of 4.8 years). (iv) We justify the use of the proposed scores for motif discovery by showing our method to outperform other motif discovery algorithms (e.g. MEME, Weeder) on benchmark datasets. We also propose new motifs on Mycobacterium tuberculosis.Availability and implementationThe method has been implemented in Java. It can be obtained from http://ls11-www.cs.tu-dortmund.de/people/marschal/paa_md/.

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Exact approaches for scaffolding.

Publications

Exact approaches for scaffolding.

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