Maximal Strip Recovery Problem with Gaps: Hardness and Approximation Algorithms

Abstract : Given two comparative maps, that is two sequences of markers each representing a genome, the Maximal Strip Recovery problem (MSR) asks to extract a largest sequence of markers from each map such that the two extracted sequences are decomposable into non-intersecting strips (or synteny blocks). This aims at defining a robust set of synteny blocks between different species, which is a key to understand the evolution process since their last common ancestor. In this paper, we add a fundamental constraint to the initial problem, which expresses the biologically sustained need to bound the number of intermediate (non-selected) markers between two consecutive markers in a strip. We therefore introduce the problem -gap-MSR, where is a (usually small) non-negative integer that upper bounds the number of non-selected markers between two consecutive markers in a strip. We show that, if we restrict ourselves to comparative maps without duplicates, the problem is polynomial for = 0, NP-complete for = 1, and APX-hard for 2. For comparative maps with duplicates, the problem is APX-hard for all 0.
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Laurent Bulteau, Guillaume Fertin, Irena Rusu. Maximal Strip Recovery Problem with Gaps: Hardness and Approximation Algorithms. Journal of Discrete Algorithms, Elsevier, 2013, 19, pp.1-22. ⟨hal-00826876⟩

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