Feasibility check for the distance geometry problem: an application to molecular conformations

Abstract : 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 models (IP) and a constraint programming (CP) approach are presented to test feasibility of the DGP. The two IP models are improved with the inclusion of valid inequalities and the CP approach is improved with the use of an algorithm to perform a domain reduction. The main motivation to 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.
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Agostinho Agra, Rosa Figueiredo, Carlile Lavor, Nelson Maculan, Antonio Pereira, et al.. Feasibility check for the distance geometry problem: an application to molecular conformations. International Transactions in Operational Research, Wiley, 2017, 24 (5), pp.1023-1040. ⟨10.1111/itor.12283⟩. ⟨hal-02179703⟩

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