Paper by Erik D. Demaine

Daniel Kane, Gregory N. Price, and Erik D. Demaine, “A pseudopolynomial algorithm for Alexandrov's Theorem”, in Proceedings of the 11th Algorithms and Data Structures Symposium (WADS 2009), Lecture Notes in Computer Science, volume 5664, Banff, Alberta, Canada, August 21–23, 2009, pages 435–446.

Alexandrov's Theorem states that every metric with the global topology and local geometry required of a convex polyhedron is in fact the intrinsic metric of some convex polyhedron. Recent work by Bobenko and Izmestiev describes a differential equation whose solution is the polyhedron corresponding to a given metric. We describe an algorithm based on this differential equation to compute the polyhedron to arbitrary precision given the metric, and prove a pseudopolynomial bound on its running time.

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The paper is 12 pages.

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Last updated March 12, 2024 by Erik Demaine.