Article ID Journal Published Year Pages File Type
6423681 Electronic Notes in Discrete Mathematics 2016 6 Pages PDF
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. We first characterize the existence of shortcut sets, and compute shortcut sets in polynomial time providing an upper bound on their size. Then, we analyze the role of the convex hull of Nℓ when inserting a shortcut set. As a main result, we prove that one can always determine in polynomial time whether inserting only one segment suffices to reduce the diameter.

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Related Topics
Physical Sciences and Engineering Mathematics Discrete Mathematics and Combinatorics
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