Discrete & Computational Geometry
, Volume 12, Issue 3, pp 241261
First online:
Hellytype theorems and Generalized Linear Programming
 N. AmentaAffiliated withComputer Science, University of CaliforniaThe Geometry Center
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Recent combinatorial algorithms for linear programming can also be applied to certain nonlinear problems. We call these Generalized LinearProgramming, or GLP, problems. We connect this class to a collection of results from combinatorial geometry called Hellytype theorems. We show that there is a Hellytype theorem about the constraint set of every GLP problem. Given a familyH of sets with a Hellytype theorem, we give a paradigm for finding whether the intersection ofH is empty, by formulating the question as a GLP problem. This leads to many applications, including linear expected time algorithms for finding line transversals and minimax hyperplane fitting. Our applications include GLP problems with the surprising property that the constraints are nonconvex or even disconnected.
 Title
 Hellytype theorems and Generalized Linear Programming
 Journal

Discrete & Computational Geometry
Volume 12, Issue 3 , pp 241261
 Cover Date
 199409
 DOI
 10.1007/BF02574379
 Print ISSN
 01795376
 Online ISSN
 14320444
 Publisher
 Springer New York
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 Authors

 N. Amenta ^{(1)} ^{(2)}
 Author Affiliations

 1. Computer Science, University of California, 94720, Berkeley, CA, USA
 2. The Geometry Center, 55454, Minneapolis, MN, USA