Paper by Erik D. Demaine

Prosenjit Bose, Erik D. Demaine, Ferran Hurtado, John Iacono, Stefan Langerman, and Pat Morin, “Geodesic Ham-Sandwich Cuts”, in Proceedings of the 20th Annual ACM Symposium on Computational Geometry (SoCG 2004), Brooklyn, New York, June 9–11, 2004, pages 1–9.

Let P be a simple polygon with m vertices, k of which are reflex, and which contains r red points and b blue points in its interior. Let n = m + r + b. A ham-sandwich geodesic is a shortest path in P between any two points on the boundary of P that simultaneously bisects the red points and the blue points. We present an O(n log k)-time algorithm for finding a ham-sandwich geodesic. We also show that this algorithm is optimal in the algebraic computation tree model when parameterizing the running time with respect to n and k.

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The paper is 9 pages.

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Related papers:
GeodesicHamSandwich_DCG (Geodesic Ham-Sandwich Cuts)

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Last updated July 23, 2024 by Erik Demaine.