A Pseudopolynomial Algorithm for Alexandrov's Theorem Export

@article{citeulike:3890437, 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.}, archivePrefix = {arXiv}, author = {Kane, Daniel and Price, Gregory N. and Demaine, Erik D.}, citeulike-article-id = {3890437}, citeulike-linkout-0 = {http://arxiv.org/abs/0812.5030}, citeulike-linkout-1 = {http://arxiv.org/pdf/0812.5030}, day = {30}, eprint = {0812.5030}, keywords = {aleksandrov, algorithm, convex, convex-polyhedron, minkowski}, month = {Dec}, posted-at = {2009-01-16 09:14:54}, priority = {2}, title = {A Pseudopolynomial Algorithm for Alexandrov's Theorem}, url = {http://arxiv.org/abs/0812.5030}, year = {2008} }

TY - JOUR ID - citeulike:3890437 L3 - citeulike-article-id:3890437 N2 - 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. TI - A Pseudopolynomial Algorithm for Alexandrov's Theorem KW - aleksandrov KW - algorithm KW - convex KW - convex-polyhedron KW - minkowski AU - Kane, Daniel AU - Price, Gregory AU - Demaine, Erik PY - 2008/Dec/30/ UR - http://arxiv.org/abs/0812.5030 ER -