Maximal strip recovery problem with gaps: Hardness and approximation algorithms

  • Authors:

  • Laurent Bulteau;Guillaume Fertin;Irena Rusu

  • Affiliations:

  • Laboratoire dInformatique de Nantes-Atlantique (LINA), UMR CNRS 6241, Université de Nantes, 2 rue de la Houssinière, 44322 Nantes Cedex 3, France;Laboratoire dInformatique de Nantes-Atlantique (LINA), UMR CNRS 6241, Université de Nantes, 2 rue de la Houssinière, 44322 Nantes Cedex 3, France;Laboratoire dInformatique de Nantes-Atlantique (LINA), UMR CNRS 6241, Université de Nantes, 2 rue de la Houssinière, 44322 Nantes Cedex 3, France

  • Venue:
  • Journal of Discrete Algorithms
  • Year:
  • 2013

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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 @d-gap-MSR, where @d 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 @d=0, NP-complete for @d=1, and APX-hard for @d=2. For comparative maps with duplicates, the problem is APX-hard for all @d=0.