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UBC Theses and Dissertations

On competitive strategies for external exploration of a convex polygon Clarkson, Kyle P.

Abstract

In this thesis we consider the problem faced by an agent who is tasked with inspecting certain objects within the plane. In particular, given some starting position not interior to a convex polygon the agent must traverse through the plane to fully see all edges of the polygon. However traversal is expensive for the agent and so the agent would like to determine the shortest path it can take such that all edges of the polygon will be seen from the path. For all polygons and feasible starting positions we present an efficient algorithm for determining what the shortest path is by characterizing properties that any such path must exhibit. Next we consider how the agent should accomplish this task when it is only aware that the polygon it is to inspect is convex, but not its shape (i.e. location of edges.) In such a scenario the agent must search for the edges by traversing through the plane. Yet if such searching is not done in an efficient manner, the distance traversed may be unacceptably large with respect to the length of the optimal path. We discuss several strategies that the agent can employ that will ensure that the distance it traverses to see all edges is at most a constant times the length of the optimal path.

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Attribution-NonCommercial-NoDerivatives 4.0 International

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