A Pseudopolynomial Algorithm for Alexandrov's Theorem

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. G. Price was partially supported by an NSF Graduate Research Fellowship. E. Demaine was partially supported by NSF CAREER award CCF-0347776. 

• Type: Conference
• Year: 2009
• Where: WADS
• Authors: Daniel M. Kane, Gregory N. Price, Erik D. Demaine
• Keywords: Algorithms, Convex Polyhedron, Differential Equation, Intrinsic Metric, WADS 2009