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On the Exact Solution of the Distance Geometry with Interval Distances in Dimension 1

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Recent Advances in Computational Optimization

Part of the book series: Studies in Computational Intelligence ((SCI,volume 717))

Abstract

Distance Geometry consists in embedding a simple weighted undirected graph in a given space so that the distances between embedded vertices correspond to the edge weights. Weights can be either exact real values, or real-valued intervals. In this work, the focus is on problems where the embedding space is the Euclidean 1-dimensional space, and the general situation where distances can be represented by intervals is taken into consideration. A previously proposed branch-and-prune algorithm is adapted to the 1-dimensional case, and the proposed variant turns out to be deterministic even in presence of interval distances. Backtracking pruning is introduced in the algorithm for guaranteeing that all vertex positions in a given solution are actually feasible. The proposed algorithm is tested on a set of artificially generated instances in dimension 1.

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Acknowledgements

The author is thankful to the anonymous referees.

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Authors and Affiliations

  1. IRISA, University of Rennes 1, Rennes, France

    Antonio Mucherino

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  1. Antonio Mucherino
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Correspondence to Antonio Mucherino .

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Editors and Affiliations

  1. Department of Parallel Algorithms, Institute of Information and Communication Technology, Bulgarian Academy of Sciences , Sofia, Bulgaria

    Stefka Fidanova

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Mucherino, A. (2018). On the Exact Solution of the Distance Geometry with Interval Distances in Dimension 1. In: Fidanova, S. (eds) Recent Advances in Computational Optimization. Studies in Computational Intelligence, vol 717. Springer, Cham. https://doi.org/10.1007/978-3-319-59861-1_8

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  • DOI: https://doi.org/10.1007/978-3-319-59861-1_8

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-59860-4

  • Online ISBN: 978-3-319-59861-1

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