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A Pseudopolynomial Algorithm for Alexandrov's Theorem

Authors Daniel Kane, Gregory Nathan Price, Erik Demaine

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Daniel Kane
Gregory Nathan Price
Erik Demaine

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Daniel Kane, Gregory Nathan Price, and Erik Demaine. A Pseudopolynomial Algorithm for Alexandrov's Theorem. In Computational Geometry. Dagstuhl Seminar Proceedings, Volume 9111, pp. 1-22, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2009)


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 given the metric, and prove a pseudopolynomial bound on its running time.
  • Folding
  • metrics
  • pseudopolynomial
  • algorithms


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