# Constraint Programming Approaches to the Discretizable Molecular Distance Geometry Problem

## TL;DR

This paper introduces new constraint programming methods for solving the Discretizable Molecular Distance Geometry Problem, improving over existing integer programming approaches in efficiency and effectiveness.

## Contribution

It presents the first constraint programming formulations for the problem, along with techniques for infeasibility checks, domain reduction, and symmetry breaking.

## Key findings

- Formulations outperform state-of-the-art integer programming methods
- Effective infeasibility checks and domain reduction techniques
- Improved solution times for both feasible and infeasible instances

## Abstract

The Distance Geometry Problem (DGP) seeks to find positions for a set of points in geometric space when some distances between pairs of these points are known. The so-called discretization assumptions allow to discretize the search space of DGP instances. In this paper, we study the Discretizable Molecular Distance Geometry Problem whose feasible solutions provide a discretization scheme for the DGP. We propose the first constraint programming formulations as well as a set of checks for proving infeasibility, domain reduction techniques, symmetry breaking constraints and valid inequalities. Our computational results indicate that our formulations outperform the state-of-the-art integer programming formulations, both for feasible and infeasible instances.