A Pseudo de Bruijn Graph Representation for Discretization Orders for Distance Geometry
Résumé
Instances of the distance geometry can be represented by a simple weighted undirected graph G. Vertex orders on such graphs are discretization orders if they allow for the discretization of the K-dimensional search space of the distance geometry. A pseudo de Bruijn graph B associated to G is proposed in this paper, where vertices correspond to (K+1)-cliques of G, and there is an arc from one vertex to another if, and only if, they admit an overlap, consisting of K vertices of G. This pseudo de Bruijn graph B can be exploited for constructing discretization orders for G for which the consecutivity assumption is satisfied. A new atomic order for protein backbones is presented, which is optimal in terms of length.