Computing Optimal Shortcuts for Networks
We study augmenting a plane Euclidean network with a segment, called shortcut, to minimize the largest distance between any two points along the edges of the resulting network. Questions of this type have received considerable attention recently, mostly for discrete variants of the problem. We study a fully continuous setting, where all points on the network and the inserted segment must be taken into account. We present the first results on the computation of optimal shortcuts for general networks in this model, together with several results for networks that are paths, restricted to two types of shortcuts: shortcuts with a fixed orientation and simple shortcuts.
graph augmentation
shortcut
diameter
geometric graph
Theory of computation~Computational geometry
15:1-15:12
Regular Paper
D. G. and R. S. were supported by project MTM2015-63791-R. R. S. was also supported by Gen. Cat. 2017SGR1640 and MINECO through the Ramón y Cajal program. A. M. was supported by project BFU2016-74975-P.
https://arxiv.org/abs/1807.10093
Delia
Garijo
Delia Garijo
Departamento de Matemática Aplicada I, Universidad de Sevilla, Spain
Alberto
Márquez
Alberto Márquez
Departamento de Matemática Aplicada I, Universidad de Sevilla, Spain
Natalia
Rodríguez
Natalia Rodríguez
Departamento de Computación, Universidad de Buenos Aires, Argentina
Rodrigo I.
Silveira
Rodrigo I. Silveira
Departament de Matemàtiques, Universitat Politècnica de Catalunya, Spain
10.4230/LIPIcs.ISAAC.2018.15
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Delia Garijo, Alberto Márquez, Natalia Rodríguez, and Rodrigo I. Silveira
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