Best algorithm for convex hull membership problem

Asked Dec 08 '20 at 16:22

Active Dec 09 '20 at 12:45

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Given a point $p \in \Bbb R^d$ and a finite set $S \subset \Bbb R^d$, I would like to determine if $p$ lies in the convex hull of $S$.

A literature search informed me that there are a lot of different decision procedures. Complexity-wise, what is the best known algorithm for this problem?

edited Dec 09 '20 at 12:45

Rodrigo de Azevedo

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asked Dec 08 '20 at 16:22

Luna

How is the set $S$ defined? If it is a finite set, you can formulate this as a linear optimization problem, which can be solved in polynomial time. – LinAlg Dec 08 '20 at 16:30
Yes, it is a finite set! How exactly do you formulate this as a linear optimization problem? – Luna Dec 09 '20 at 12:41
1

Does this answer your question? Test if point is in convex hull of $n$ points – Rodrigo de Azevedo Dec 09 '20 at 12:54
Yes, it does! Thank you! – Luna Dec 09 '20 at 13:05
https://mathoverflow.net/q/11508/91764 – Rodrigo de Azevedo Dec 09 '20 at 13:12
So what is the best linear optimization algorithm complexitywise? – Luna Dec 09 '20 at 14:34
@Luna That question would merit a question of its own. – Rodrigo de Azevedo Dec 09 '20 at 14:36

Best algorithm for convex hull membership problem

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