Shortcut sets for the locus of plane Euclidean networks

José Cáceres, Delia Garijo, Antonio González, Alberto Márquez, María Luz Puertas and Paula Ribeiro

Applied Mathematics and Computation, 2018, vol. 334, issue C, 192-205

Abstract: We study the problem of augmenting the locus Nℓ of a plane Euclidean network N by inserting iteratively a finite set of segments, called shortcut set, while reducing the diameter of the locus of the resulting network. There are two main differences with the classical augmentation problems: the endpoints of the segments are allowed to be points of Nℓ as well as points of the previously inserted segments (instead of only vertices of N), and the notion of diameter is adapted to the fact that we deal with Nℓ instead of N. This increases enormously the hardness of the problem but also its possible practical applications to network design. Among other results, we characterize the existence of shortcut sets, compute them in polynomial time, and analyze the role of the convex hull of Nℓ when inserting a shortcut set. Our main results prove that, while the problem of minimizing the size of a shortcut set is NP-hard, one can always determine in polynomial time whether inserting only one segment suffices to reduce the diameter.

Keywords: Euclidean network; Diameter; Shortcut set; Network design; Augmentation problem (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:334:y:2018:i:c:p:192-205

DOI: 10.1016/j.amc.2018.04.010

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