Convergence-radius conjecture for STARLINK temporal visibility graphs

Let nn be the number of nodes, and let a sub-TVG be a randomly sampled sub-temporal visibility graph of the STARLINK satellite system. Let rr denote the convergence radius of its Kleene star, meaning the radius at which the Kleene-star sequence converges. Convergence-radius conjecture. With high probability as nn\to\infty, a randomly sampled sub-TVG of STARLINK has a Kleene star that converges for r5r\leq 5 (weak version), and with high probability it has a Kleene star that converges at r=3r=3 (strong version). The conjecture concerns the asymptotic behavior of the Kleene star for increasingly large STARLINK systems; simulations suggest convergence radii below 77, while geometric considerations indicate the limiting value should be 33.

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Primary source

William Bernardoni, Robert Cardona, Jacob Cleveland, Justin Curry, Robert Green, Brian Heller, Alan Hylton, Tung Lam and Robert Kassouf-Short, “Algebraic and Geometric Models for Space Networking”, arXiv:2304.01150 (2023).

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