# Reducing Isotropy and Volume to KLS: An $O(n^3\psi^2)$ Volume Algorithm

@inproceedings{Jia2020ReducingIA, title={Reducing Isotropy and Volume to KLS: An \$O(n^3\psi^2)\$ Volume Algorithm}, author={He Jia and Aditi Laddha and Y. Lee and S. Vempala}, year={2020} }

We show that the the volume of a convex body in R in the general membership oracle model can be computed with Õ(nψ/ε) oracle queries, where ψ is the KLS constant. With the current bound of ψ . n 1 4 , this gives an Õ(n/ε) algorithm, the first general improvement on the Lovász-Vempala Õ(n/ε) algorithm from 2003. The main new ingredient is an Õ(nψ) algorithm for isotropic transformation, following which we can apply the Õ(n/ε) volume algorithm of Cousins and Vempala for well-rounded convex bodies… Expand

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