Traveling in randomly embedded random graphs
Alan Frieze, Wesley Pegden
TL;DR
This paper studies the problem of traveling among randomly embedded points in Euclidean space with randomly available connections, establishing connectivity thresholds and extending classical TSP results to this probabilistic geometric setting.
Contribution
It introduces a threshold for connectivity and generalizes the TSP length results to randomly connected Euclidean points.
Findings
Identifies a threshold for geodesic connectivity between points.
Extends the Beardwood-Halton-Hammersley theorem to random geometric graphs.
Analyzes the minimal Traveling Salesperson Tour length in this setting.
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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