On the sound covering cycle problem in paired de Bruijn graphs

Abstract

Paired de Bruijn graphs are a variant of classic de Bruijn graphs used in genome assembly. In these graphs, each vertex v is associated with two labels L(v) and R(v). We study the NP-hard SOUND COVERING CYCLE problem which has as input a paired de Bruijn graph G and two integers d and ℓ, and the task is to find a length-ℓ cycle C containing all arcs of G such that for every vertex v in C and the vertex u which occurs exactly d positions after v in C, we have R(v) = L(u). We present the first exact algorithms for this problem and several variants.