{"id":{"repo_id":"mit","oai_identifier":"oai:dspace.mit.edu:1721.1/44738"},"canonical_url":"https://search.dev.ndltd.org/etd/mit/oai:dspace.mit.edu:1721.1/44738","repository":{"repo_id":"mit","name":"MIT","base_url":"https://dspace.mit.edu/oai/request"},"display":{"title":"A pseudopolynomial algorithm for Alexandrov's theorem","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 given the metric, and prove a pseudopolynomial bound on its running time. This is joint work with Erik Demaine and Daniel Kane.","abstract_html":"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.","abstract_has_math":false,"creators":["Price, Gregory Nathan"],"institution":"Massachusetts Institute of Technology","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":"Massachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science.","school":null,"contributors":[],"advisors":["Eric D. Demaine."],"committee_chairs":[],"committee_members":[],"year":2008,"date_issued":"2008","date_published":"2008","updated_at":"2026-07-22T22:22:28Z","subjects":["Electrical Engineering and Computer Science."],"languages":["eng"],"rights":["M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission."],"rights_urls":["http://dspace.mit.edu/handle/1721.1/7582"],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/1721.1/44738","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Eric D. Demaine."]},{"key":"dc:contributor.department","label":"Department","values":["Massachusetts Institute of Technology. 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They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission."]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://dspace.mit.edu/handle/1721.1/7582"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/1721.1/44738"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2008.","Includes bibliographical references (p. 43-44)."]},{"key":"dc:description.abstract","label":"Abstract","values":["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."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["S.M."]},{"key":"dc:title","label":"Title","values":["A pseudopolynomial algorithm for Alexandrov's theorem"]}]}],"canonical_facts":{"dc:contributor.advisor":["Eric D. Demaine."],"dc:contributor.department":["Massachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science."],"dc:contributor.other":["Massachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science."],"dc:creator":["Price, Gregory Nathan"],"dc:date.accessioned":["2009-03-16T19:36:27Z"],"dc:date.available":["2009-03-16T19:36:27Z"],"dc:date.issued":["2008"],"dc:description":["Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2008.","Includes bibliographical references (p. 43-44)."],"dc:description.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 given the metric, and prove a pseudopolynomial bound on its running time. This is joint work with Erik Demaine and Daniel Kane."],"dc:description.degree":["S.M."],"dc:identifier.uri":["http://hdl.handle.net/1721.1/44738"],"dc:language.iso":["eng"],"dc:publisher":["Massachusetts Institute of Technology"],"dc:rights":["M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission."],"dc:rights.uri":["http://dspace.mit.edu/handle/1721.1/7582"],"dc:subject":["Electrical Engineering and Computer Science."],"dc:title":["A pseudopolynomial algorithm for Alexandrov's theorem"],"dc:type":["Thesis"]},"updated_at":"2026-07-22T22:22:28Z"}