Heat flow and a faster algorithm to compute the surface area of a convex body


  • This is a journal version of a conference paper [2] which appeared in FOCS 2006.


We draw on the observation that the amount of heat diffusing outside of a heated body in a short period of time is proportional to its surface area, to design a simple algorithm for approximating the surface area of a convex body given by a membership oracle. Our method has a complexity of O*(n4), where n is the dimension, compared to O*(n8) for the previous best algorithm. We show that our complexity cannot be improved given the current state-of-the-art in volume estimation. © 2013 Wiley Periodicals, Inc. Random Struct. Alg., 43, 407–428, 2013