Corpus ID: 220968699

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

  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},
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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  • Y. Lee, S. Vempala
  • Mathematics, Computer Science
  • 2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS)
  • 2017
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