Edge minimization in de Bruijn graphs

This paper introduces the de Bruijn graph edge minimization problem, which is related to the compression of de Bruijn graphs: find the order-k de Bruijn graph with minimum edge count among all orders. We describe an efficient algorithm that solves this problem. Since the edge minimization problem is connected to the BWT compression technique called tunneling, the paper also describes a way to minimize the length of a tunneled BWT in such a way that useful properties for sequence analysis are preserved. This also gives an affirmative answer to the open problem of finding optimal disjoint blocks that minimize space, as stated in Alanko et al. (DCC 2019).