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Line-of-Sight Pursuit and Evasion Games on Polytopes in R^n

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 Rn, 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. We also show that some more general classes of polytopes (monotone products) do not admit a deterministic winning Pursuer strategy. 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.

Identiferoai:union.ndltd.org:CLAREMONT/oai:scholarship.claremont.edu:hmc_theses-1082
Date01 January 2016
CreatorsPhillpot, John
PublisherScholarship @ Claremont
Source SetsClaremont Colleges
Detected LanguageEnglish
Typetext
Formatapplication/pdf
SourceHMC Senior Theses
Rights© 2016 John E Phillpot, default

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