Geometric optimization and sums of algebraic functions

Handle URI:
http://hdl.handle.net/10754/577071
Title:
Geometric optimization and sums of algebraic functions
Authors:
Vigneron, Antoine E. ( 0000-0003-3586-3431 )
Abstract:
We 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.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Computer Science Program; Visual Computing Center (VCC)
Publisher:
Association for Computing Machinery (ACM)
Journal:
ACM Transactions on Algorithms
Issue Date:
1-Jan-2014
DOI:
10.1145/2532647
Type:
Article
ISSN:
1549-6325
Appears in Collections:
Articles; Computer Science Program; Visual Computing Center (VCC); Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorVigneron, Antoine E.en
dc.date.accessioned2015-09-10T09:28:26Zen
dc.date.available2015-09-10T09:28:26Zen
dc.date.issued2014-01-01en
dc.identifier.issn1549-6325en
dc.identifier.doi10.1145/2532647en
dc.identifier.urihttp://hdl.handle.net/10754/577071en
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.en
dc.publisherAssociation for Computing Machinery (ACM)en
dc.titleGeometric optimization and sums of algebraic functionsen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.contributor.departmentComputer Science Programen
dc.contributor.departmentVisual Computing Center (VCC)en
dc.identifier.journalACM Transactions on Algorithmsen
kaust.authorVigneron, Antoine E.en
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