TCS+ Talk

Wednesday March 6, 2019 10:00 AM

Strongly log concave polynomials, high dimensional simplicial complexes, and an FPRAS for counting Bases of Matroids

Speaker: Shayan Oveis Gharan, University of Washington
Location: Annenberg 322

Abstract:

A matroid is an abstract combinatorial object which generalizes the notions of spanning trees, and linearly independent sets of vectors. I will talk about an efficient algorithm based on the Markov Chain Monte Carlo technique to approximately count the number of bases of any given matroid.

The proof is based on a new connections between high dimensional simplicial complexes, and a new class of multivariate polynomials called completely log-concave polynomials. In particular, we exploit a fundamental fact from our previous work that the bases generating polynomial of any given matroid is a log-concave function over the positive orthant.

Based on joint works with Nima Anari, Kuikui Liu, and Cynthia Vinzant.

Series TCS+ Talks

Contact: Bonnie Leung bjleung@caltech.edu