Suppose now I have 1000 d-dimensional data points. Is there a convenient algorithm that can approximate the volume of the concave/convex hull formed by these points?
Thanks in advance!
2026-03-31 12:13:37.1774959217
Algorithms that approximate the volume of concave/convex hull formed by some n-dimensional data points
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According to Wikipedia, given a membership oracle, we can compute an $\epsilon$ approximation of the volume of the convex hull in polynomial time in $n$ (=1000), $d$ and $\frac{1}{\epsilon}$.
Combining with this answer, it seems that membership can also be tested fairly quickly. However, if this is convenient enough for you, I don't know.