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dc.contributor.authorVigneron, Antoine E.
dc.date.accessioned2015-09-10T09:28:26Z
dc.date.available2015-09-10T09:28:26Z
dc.date.issued2014-01-01
dc.identifier.citationVigneron, A. (2014). Geometric optimization and sums of algebraic functions. ACM Transactions on Algorithms, 10(1), 1–20. doi:10.1145/2532647
dc.identifier.issn1549-6325
dc.identifier.doi10.1145/2532647
dc.identifier.urihttp://hdl.handle.net/10754/577071
dc.description.abstractWe present a new optimization technique that yields the first FPTAS for several geometric problems. These problems reduce to optimizing a sum of nonnegative, constant description complexity algebraic functions. We first give an FPTAS for optimizing such a sum of algebraic functions, and then we apply it to several geometric optimization problems. We obtain the first FPTAS for two fundamental geometric shape-matching problems in fixed dimension: maximizing the volume of overlap of two polyhedra under rigid motions and minimizing their symmetric difference. We obtain the first FPTAS for other problems in fixed dimension, such as computing an optimal ray in a weighted subdivision, finding the largest axially symmetric subset of a polyhedron, and computing minimum-area hulls.
dc.publisherAssociation for Computing Machinery (ACM)
dc.titleGeometric optimization and sums of algebraic functions
dc.typeArticle
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.departmentComputer Science Program
dc.contributor.departmentVisual Computing Center (VCC)
dc.identifier.journalACM Transactions on Algorithms
kaust.personVigneron, Antoine E.


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