Deterministic approximate counting of matchings and independent sets in sparse graphs
- LecturerProf. Yitong Yin (Department of Computer Science and Technology, Nanjing University.)
Host: Kai-Min Chung - Time2014-12-19 (Fri.) 16:30 ~ 17:30
- LocationAuditorium 126 at CITI Building
Abstract
I will talk about deterministic approximate counting of matchings and independent sets in graphs of bounded connective constant. More generally, we consider the problem of evaluating the partition functions of the monomer-dimer model (weighted matchings) and the hard core model (weighted independent sets). The connective constant is a natural measure of the average degree of a graph which has been studied extensively in combinatorics and mathematical physics, and can be bounded by a constant even for certain unbounded degree graphs such as those sampled from the sparse Erdős–Rényi model G(n, d/n).
Our main technical contribution is to prove the best possible rates of decay of correlations in the natural probability distributions induced by both the hard core model and the monomer-dimer model in graphs with a given bound on the connective constant. We then use these optimal decay of correlations results to obtain efficient approximation algorithms (FPTASs) for the two problems on graphs of bounded connective constant.
This is a joint work with Alistair Sinclair, Piyush Srivastava and Daniel Štefankovič (in FOCS’13 and SODA’15).
BIO
Yitong Yin is an associate professor at Nanjing University, China. He graduated with a PhD in Computer Science from Yale University in 2009. His research area is Theoretical Computer Science: in particular, randomized algorithms, and data structure lower bounds.