Complexity and Polynomial-Time Approximation Algorithms around the Scaffolding Problem

Annie Chateau (1) , Rodolphe Giroudeau (2)

1 MAB - Méthodes et Algorithmes pour la Bioinformatique
2 MAORE - Methods, Algorithms for Operations REsearch

We explore in this paper some complexity issues inspired by the contig scaffolding problem in bioinformatics. We focus on the following problem: given an undirected graph with no loop, and a perfect matching on this graph, find a set of cycles and paths covering every vertex of the graph, with edges alternatively in the matching and outside the matching, and satisfying a given constraint on the numbers of cycles and paths. We show that this problem is NP-complete, even in bipartite graphs. We also exhibit non-approximability and polynomial-time approximation results, in the optimization versions of the problem.

Mots clés: Scaffolding; Polynomial-Time Approximation; Complexity

Domaines: Complexité [cs.CC]; Bio-informatique [q-bio.QM]

Annie Chateau, Rodolphe Giroudeau. Complexity and Polynomial-Time Approximation Algorithms around the Scaffolding Problem. AlCoB: Algorithms for Computational Biology, Jul 2014, Tarragona, Spain. pp.47-58, ⟨10.1007/978-3-319-07953-0_4⟩. ⟨lirmm-01007556⟩