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arXiv · 1411.6596

Traveling in randomly embedded random graphs

Alan Frieze·Wesley Pegden
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Abstract

We consider the problem of traveling among random points in Euclidean space, when only a random fraction of the pairs are joined by traversable connections. In particular, we show a threshold for a pair of points to be connected by a geodesic of length arbitrarily close to their Euclidean distance, and analyze the minimum length Traveling Salesperson Tour, extending the Beardwood-Halton-Hammersley theorem to this setting.

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Alan Frieze, Wesley Pegden. 2014-11-24. Traveling in randomly embedded random graphs. https://arxiv.org/abs/1411.6596

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