Heat Flow and a Faster Algorithm to Compute the Surface Area of a Convex Body

  • Authors:

  • Mikhail Belkin;Hariharan Narayanan;Partha Niyogi

  • Affiliations:

  • Ohio State University, USA;University of Chicago, USA;University of Chicago, USA

  • Venue:
  • FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
  • Year:
  • 2006

  • Sampling Hypersurfaces through Diffusion

    APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques

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Abstract

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*(n^4), where n is the dimension, compared to O*(n^8.5) for the previous best algorithm. We show that our complexity cannot be improved given the current state-of-the-art in volume estimation.