A new algorithm for the $^K$DMDGP subclass of Distance Geometry Problems

TL;DR

This paper introduces a new algorithm for the DMDGP subclass of the Distance Geometry Problem that leverages symmetry properties to significantly improve computational efficiency, especially in protein conformation applications.

Contribution

The paper presents a novel algorithm that more effectively exploits DMDGP symmetries, enhancing the efficiency of solving sparse instances compared to previous Branch-and-Prune methods.

Findings

Significant speedup over classic BP algorithm for sparse DMDGP instances

Effective exploitation of symmetry properties improves search efficiency

Applicable to protein conformation problems

Abstract

The fundamental inverse problem in distance geometry is the one of finding positions from inter-point distances. The Discretizable Molecular Distance Geometry Problem (DMDGP) is a subclass of the Distance Geometry Problem (DGP) whose search space can be discretized and represented by a binary tree, which can be explored by a Branch-and-Prune (BP) algorithm. It turns out that this combinatorial search space possesses many interesting symmetry properties that were studied in the last decade. In this paper, we present a new algorithm for this subclass of the DGP, which exploits DMDGP symmetries more effectively than its predecessors. Computational results show that the speedup, with respect to the classic BP algorithm, is considerable for sparse DMDGP instances related to protein conformation.