On NP-Hardness of the Paired de Bruijn Sound Cycle Problem

The paired de Bruijn graph is an extension of de Bruijn graph incorporating mate pair information for genome assembly proposed by Mevdedev et al. However, unlike in an ordinary de Bruijn graph, not every path or cycle in a paired de Bruijn graph will spell a string, because there is an additional soundness constraint on the path. In this paper we show that the problem of checking if there is a sound cycle in a paired de Bruijn graph is NP-hard in general case. We also explore some of its special cases, as well as a modified version where the cycle must also pass through every edge.