eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Open Access Series in Informatics
2190-6807
2019-01-08
9:1
9:14
10.4230/OASIcs.SOSA.2019.9
article
Asymmetric Convex Intersection Testing
Barba, Luis
Mulzer, Wolfgang
We consider asymmetric convex intersection testing (ACIT).
Let P subset R^d be a set of n points and H a set of n halfspaces in d dimensions. We denote by {ch(P)} the polytope obtained by taking the convex hull of P, and by {fh(H)} the polytope obtained by taking the intersection of the halfspaces in H. Our goal is to decide whether the intersection of H and the convex hull of P are disjoint. Even though ACIT is a natural variant of classic LP-type problems that have been studied at length in the literature, and despite its applications in the analysis of high-dimensional data sets, it appears that the problem has not been studied before.
We discuss how known approaches can be used to attack the ACIT problem, and we provide a very simple strategy that leads to a deterministic algorithm, linear on n and m, whose running time depends reasonably on the dimension d.
https://drops.dagstuhl.de/storage/01oasics/oasics-vol069-sosa2019/OASIcs.SOSA.2019.9/OASIcs.SOSA.2019.9.pdf
polytope intersection
LP-type problem
randomized algorithm