Computer Science/Discrete Mathematics Seminar I

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

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.

Date & Time

February 25, 2019 | 11:00am – 12:00pm

Location

Simonyi Hall 101

Speakers

Shayan Oveis Gharan

Affiliation

University of Washington