New Polynomial-Time Algorithm around the Scaffolding Problem

International audienceWe describe in this paper an approximation algorithm for the scaffolding problem, which is part of genome inference in bioinformatics. The aim of the problem is to find a maximum weighted collection of disjoint alternating cycles and paths covering a particular graph called scaffold graph. The problem is known to be NP-complete, and we describe further result concerning a special class of graphs aiming to be close to real instances. The described algorithm is the first polynomial-time approximation algorithm designed for this problem on non-complete graphs

Linearizing Genomes: Exact Methods and Local Search

International audienceIn this article, we address the problem of genome linearization from the perspective of Polynomial Local Search, a complexity class related to finding local optima. We prove that the linearization problem, with a neighborhood structure, the neighbor slide, is PLS-complete. On the positive side, we develop two exacts methods, one using tree decompositions with an efficient dynamic programming, the other one using an integer linear program. Finally, we compare them on real instances