A Time-space Trade-off for Computing the Geodesic Center of a Simple Polygon

08/29/2019

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by   Pardis Kavand, et al.

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In this paper we study the problem of computing the geodesic center of a simple polygon when the available workspace is limited. For an n-vertex simple polygon, we give a time-space trade-off algorithm that finds the geodesic center in O(T(n, s) log^2 n+ n^2/slog n) expected time and uses O(s) additional words of space where s∈Ω(log n) ∩ O(n), and T(n, s) is the time needed for constructing the shortest path tree of a given point inside a simple polygon, in depth-first order, with O(s) extra space. Applying the best current known time-space trade-off of Oh and Ahn (Algorithmica 2019) for shortest path tree, our algorithm runs in O(n^2/slog^3 n) expected time.