A Clifford Algebra approach to the Discretizable Molecular Distance Geometry Problem

TL;DR

This paper introduces a novel Clifford Algebra model for the Discretizable Molecular Distance Geometry Problem and adapts the Branch & Prune algorithm to leverage this algebraic framework, enhancing the problem-solving approach.

Contribution

It presents the first Clifford Algebra-based model for DMDGP and modifies the BP algorithm to utilize this algebraic structure, offering a new perspective and potential efficiency improvements.

Findings

Clifford Algebra provides a new mathematical framework for DMDGP.

The adapted BP algorithm demonstrates effective problem-solving capabilities.

The approach offers a promising direction for molecular distance geometry computations.

Abstract

The Discretizable Molecular Distance Geometry Problem (DMDGP) consists in a subclass of the Molecular Distance Geometry Problem for which an embedding in ${\mathbb{R}^3}$ can be found using a Branch & Prune (BP) algorithm in a discrete search space. We propose a Clifford Algebra model of the DMDGP with an accompanying version of the BP algorithm.