Maximal Strip Recovery Problem with Gaps: Hardness and Approximation Algorithms

  • Authors:

  • Laurent Bulteau;Guillaume Fertin;Irena Rusu

  • Affiliations:

  • École Normale Supérieure, Paris, France 75000 and Laboratoire d'Informatique de Nantes-Atlantique (LINA), UMR CNRS 6241 Université de Nantes, Nantes Cedex 3, France 44322;Laboratoire d'Informatique de Nantes-Atlantique (LINA), UMR CNRS 6241 Université de Nantes, Nantes Cedex 3, France 44322;Laboratoire d'Informatique de Nantes-Atlantique (LINA), UMR CNRS 6241 Université de Nantes, Nantes Cedex 3, France 44322

  • Venue:
  • ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
  • Year:
  • 2009

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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-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 驴-gap-MSR, where 驴 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 驴-gap-MSR is NP-complete for any 驴 驴 1, and even APX-hard for any 驴 驴 2. We also provide two approximation algorithms, with ratio 1.8 for 驴= 1, and ratio 4 for 驴 驴 2.