A pseudopolynomial algorithm for Alexandrov's theorem
Author(s)Price, Gregory Nathan
pseudopolynomial-time construction for Alexandrov's theorem
Massachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science.
Eric D. Demaine.
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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. This is joint work with Erik Demaine and Daniel Kane.
Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2008.Includes bibliographical references (p. 43-44).
DepartmentMassachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science.
Massachusetts Institute of Technology
Electrical Engineering and Computer Science.