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-overlapping 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 δ-gap-MSR, where δ is a (usually small) non-negative integer that upper bounds the number of non-selected markers between two consecutive markers in a strip. Depending on the nature of the comparative maps (i.e., with or without duplicates), we show that δ-gap-MSR is NP-complete for any δ ≥ 1, and even APX-hard for any δ ≥ 2. We also provide two approximation algorithms, with ratio 1.8 for δ= 1, and ratio 4 for δ ≥ 2.
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Bulteau, L., Fertin, G., Rusu, I. (2009). Maximal Strip Recovery Problem with Gaps: Hardness and Approximation Algorithms. In: Dong, Y., Du, DZ., Ibarra, O. (eds) Algorithms and Computation. ISAAC 2009. Lecture Notes in Computer Science, vol 5878. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10631-6_72
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DOI: https://doi.org/10.1007/978-3-642-10631-6_72
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