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Asymmetric Convex Intersection Testing

Authors Luis Barba, Wolfgang Mulzer

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  • polytope intersection
  • LP-type problem
  • randomized algorithm

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Abstract

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.

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Luis Barba and Wolfgang Mulzer. Asymmetric Convex Intersection Testing. In 2nd Symposium on Simplicity in Algorithms (SOSA 2019). Open Access Series in Informatics (OASIcs), Volume 69, pp. 9:1-9:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019) https://doi.org/10.4230/OASIcs.SOSA.2019.9

Author Details

Luis Barba
Wolfgang Mulzer

References

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