The discretizable molecular distance geometry problem

Authors:
Carlile Lavor;Leo Liberti;Nelson Maculan;Antonio Mucherino
Affiliations:
Department of Applied Mathematics (IMECC-UNICAMP), State University of Campinas, Campinas, Brazil 13081-970;LIX, École Polytechnique, Palaiseau, France 91128;Federal University of Rio de Janeiro (COPPE---UFRJ), Rio de Janeiro, Brazil 21945-970;CERFACS, Toulouse, France
Venue:
Computational Optimization and Applications
Year:
2012

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Abstract

Given a simple weighted undirected graph G=(V,E,d) with d:E驴驴+, the Molecular Distance Geometry Problem (MDGP) consists in finding an embedding x:V驴驴3 such that 驴x u 驴x v 驴=d uv for each {u,v}驴E. We show that under a few assumptions usually satisfied in proteins, the MDGP can be formulated as a search in a discrete space. We call this MDGP subclass the Discretizable MDGP (DMDGP). We show that the DMDGP is NP-hard and we propose a solution algorithm called Branch-and-Prune (BP). The BP algorithm performs remarkably well in practice in terms of speed and solution accuracy, and can be easily modified to find all incongruent solutions to a given DMDGP instance. We show computational results on several artificial and real-life instances.