Crossing Numbers and Stress of Random Graphs

08/22/2018

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by   Markus Chimani, et al.

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Consider a random geometric graph over a random point process in R^d. Two points are connected by an edge if and only if their distance is bounded by a prescribed distance parameter. We show that projecting the graph onto a two dimensional plane is expected to yield a constant-factor crossing number (and rectilinear crossing number) approximation. We also show that the crossing number is positively correlated to the stress of the graph's projection.