A Pseudopolynomial Algorithm for Alexandrov’s Theorem

  • Daniel Kane
  • Gregory N. Price
  • Erik D. Demaine
Conference paper

DOI: 10.1007/978-3-642-03367-4_38

Part of the Lecture Notes in Computer Science book series (LNCS, volume 5664)
Cite this paper as:
Kane D., Price G.N., Demaine E.D. (2009) A Pseudopolynomial Algorithm for Alexandrov’s Theorem. In: Dehne F., Gavrilova M., Sack JR., Tóth C.D. (eds) Algorithms and Data Structures. WADS 2009. Lecture Notes in Computer Science, vol 5664. Springer, Berlin, Heidelberg

Abstract

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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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Daniel Kane
    • 1
  • Gregory N. Price
    • 2
  • Erik D. Demaine
    • 2
  1. 1.Department of MathematicsHarvard UniversityCambridgeUSA
  2. 2.MIT Computer Science and Artificial Intelligence LaboratoryCambridgeUSA

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