The De Bruijn Mapping Problem with Changes in the Graph

In computational biology, mapping a sequence s onto a sequence graph G poses a significant challenge. One possible approach to tackling this problem is to find a walk p in G that spells a sequence most similar to s. This challenge is formally known as the Graph Sequence Mapping Problem (GSMP). In this paper, we delve into an alternative problem formulation known as the De Bruijn Graph Sequence Mapping Problem (BSMP). Both problems have three variants: changes only in the sequence, changes in the graph, and changes in both the sequence and the graph. We concentrate on addressing the variant involving changes in the graph. In the literature, when this problem does not allow the De Bruijn graph to induce new arcs after changes, it becomes NP-complete, as proven by Gibney et. al [4]. However, we reformulate the problem by considering the characteristics of the arcs induced in the De Bruijn graph. This reformulation alters the problem definition, thereby enabling the application of a polynomial-time algorithm for its resolution. Approaching the problem with this arc-inducing characteristic is new, and the algorithm proposed in this work is new in the literature.