An integer programming approach for the search of discretization orders in distance geometry problems

Abstract

Discretizable distance geometry problems (DDGPs) constitute a class of graph realization problems where the vertices can be ordered in such a way that the search space of possible positions becomes discrete, usually represented by a binary tree. Finding such vertex orders is an essential step to identify and solve DDGPs. Here we look for discretization orders that minimize an indicator of the size of the search tree. This paper sets the ground for exact solution of the optimal discretization order problem by proposing two integer programming formulations and a constraint generation procedure for an extended formulation. We discuss some theoretical aspects of the problem and numerical experiments on protein-like instances of DDGP are also reported.