SODA Conference 2017 Conference Paper
Approximately Sampling Elements with Fixed Rank in Graded Posets
- Prateek Bhakta
- Benjamin Cousins
- Matthew Fahrbach
- Dana Randall
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SODA Conference 2017 Conference Paper
STOC Conference 2015 Conference Paper
We present an O*(n 3 ) randomized algorithm for estimating the volume of a well-rounded convex body given by a membership oracle, improving on the previous best complexity of O*(n 4 ). The new algorithmic ingredient is an accelerated cooling schedule where the rate of cooling increases with the temperature. Previously, the known approach for potentially achieving such complexity relied on a positive resolution of the KLS hyperplane conjecture, a central open problem in convex geometry.
SODA Conference 2014 Conference Paper