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arXiv · 1304.3402

On the Average Number of Edges in Theta Graphs

Pat Morin·Sander Verdonschot
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Abstract

Theta graphs are important geometric graphs that have many applications, including wireless networking, motion planning, real-time animation, and minimum-spanning tree construction. We give closed form expressions for the average degree of theta graphs of a homogeneous Poisson point process over the plane. We then show that essentially the same bounds---with vanishing error terms---hold for theta graphs of finite sets of points that are uniformly distributed in a square. Finally, we show that the number of edges in a theta graph of points uniformly distributed in a square is concentrated around its expected value.

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Pat Morin, Sander Verdonschot. 2013-04-11. On the Average Number of Edges in Theta Graphs. https://arxiv.org/abs/1304.3402

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