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Feasibility check for the distance geometry problem: an application to molecular conformations
Author(s) -
Agra Agostinho,
Figueiredo Rosa,
Lavor Carlile,
Maculan Nelson,
Pereira António,
Requejo Cristina
Publication year - 2017
Publication title -
international transactions in operational research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.032
H-Index - 52
eISSN - 1475-3995
pISSN - 0969-6016
DOI - 10.1111/itor.12283
Subject(s) - embedding , mathematics , metric space , integer programming , graph , euclidean space , graph embedding , algorithm , discrete mathematics , computer science , theoretical computer science , combinatorics , artificial intelligence
The distance geometry problem (DGP) consists in finding an embedding in a metric space of a given weighted undirected graph such that for each edge in the graph, the corresponding distance in the embedding belongs to a given distance interval. We discuss the relationship between the existence of a graph embedding in a Euclidean space and the existence of a graph embedding in a lattice. Different approaches, including two integer programming (IP) models and a constraint programming (CP) approach, are presented to test the feasibility of the DGP. The two IP models are improved with the inclusion of valid inequalities, and the CP approach is improved using an algorithm to perform a domain reduction. The main motivation for this work is to derive new pruning devices within branch‐and‐prune algorithms for instances occurring in real applications related to determination of molecular conformations, which is a particular case of the DGP. A computational study based on a set of small‐sized instances from molecular conformations is reported. This study compares the running times of the different approaches to check feasibility.