@article{, author = {Brieden, Andreas; Gritzmann, Peter}, title = {On Helly's theorem: Extensions and Algorithms}, editor = {}, booktitle = {}, series = {}, journal = {Discrete & Computational Geometry}, address = {}, publisher = {}, edition = {}, year = {1997}, isbn = {}, volume = {17}, number = {4}, pages = {393-410 }, url = {}, doi = {10.1007/PL00009300}, keywords = {}, abstract = {This paper studies algorithmic Helly-type problems in the framework of the algorithmic theory of convex bodies developed by Grötschel, Lovász, and Schrijver. Various oracle-polynomial-time algorithms are presented that are complemented by NP-hardness results for polytopes. In addition, some new Helly-type theorems are derived.}, note = {}, institution = {Universität der Bundeswehr München, Fakultät für Wirtschafts- und Organisationswissenschaften, WOW 1 - Institut für Controlling, Finanz- und Risikomanagement, Professur: Brieden, Andreas}, }