Revisiting the Minimum Breakpoint Linearization Problem Theoretical Computer Science

Laurent Bulteau (1) , Guillaume Fertin (1) , Irena Rusu (1)

1 LINA - Laboratoire d'Informatique de Nantes Atlantique

The gene order on a chromosome is a necessary data for most comparative genomics studies, but in many cases only partial orders can be obtained by cur- rent genetic mapping techniques. The Minimum Breakpoint Linearization Problem aims at constructing a total order from this partial knowledge, such that the breakpoint distance to a reference genome is minimized. In this paper, we first expose a flaw in two algorithms formerly known for this problem [6, 4]. We then present a new modeling for this problem, and use it to design three approximation algorithms, with ratios resp. O(log(k) log log(k)), O(log2 (|X|)) and m2 + 4m − 4, where k is the optimal breakpoint distance we look for, |X| is upper bounded by the number of pair of genes for which the partial order is in contradiction with the reference genome, and m is the number of genetic maps used to create the input partial order.

Mots clés: comparative genomics; breakpoint distance; partially ordered genome; approximation algorithms

Domaines: Complexité [cs.CC]; Bio-informatique [q-bio.QM]; Bio-Informatique, Biologie Systémique [q-bio.QM]

Laurent Bulteau, Guillaume Fertin, Irena Rusu. Revisiting the Minimum Breakpoint Linearization Problem Theoretical Computer Science. Theoretical Computer Science, 2013, 494, pp.122-133. ⟨hal-00826880⟩