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John Phillpot

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Line-of-Sight Pursuit and Evasion Games on Polytopes in $\mathbb{R}^n$

Ran Libeskind-Hadas (CS)
Second Reader(s)
Nicholas J. Pippenger


We study single-pursuer, line-of-sight Pursuit and Evasion games in polytopes in $\mathbb{R}^n$. We develop winning Pursuer strategies for simple classes of polytopes (monotone prisms) in $\mathbb{R}^n$, using proven algorithms for polygons as inspiration and as subroutines. More generally, we show that any Pursuer-win polytope can be extended to a new Pursuer-win polytope in more dimensions. Though we provide bounds on which polytopes are Pursuer-win, these bounds are not tight. Closing the gap between those polytopes known to be Pursuer-win and those known not to be remains an problem for future researchers.

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