ARC Colloquium: Yitong Yin – Nanjing University

Event Details
Contact

Dani Denton
denton at cc dot gatech dot edu

 

Summaries

Summary Sentence: Klaus 1116 West at 1 pm

Full Summary: No summary paragraph submitted.

Algorithms & Randomness Center (ARC)

Yitong Yin – Nanjing University

Monday, September 28, 2015

Klaus 1116 West - 1:00 pm

(Refreshments will be served in Klaus 2222 at 2 pm)

Title:

Counting hypergraph matchings up to uniqueness threshold

Abstract:

We study the problem of approximately counting hypergraph matchings with an activity parameter $\lambda$ in hypergraphs of bounded maximum degree and bounded maximum size of hyperedges. This problem unifies two important statistical physics models in approximate counting: the hardcore model (graph independent sets) and the monomer-dimer model (graph matchings).

We show for this model the critical activity $\lambda_c= \frac{d^d}{k (d-1)^{d+1}}$ is the threshold for the uniqueness of Gibbs measures on the infinite $(d+1)$-uniform $(k+1)$-regular hypertree. And we show that when $\lambda<\lambda_c$ the model exhibits strong spatial mixing at an exponential rate and there is an FPTAS for the partition function of the model on all hypergraphs of maximum degree at most $k+1$ and maximum  edge size at most $d+1$. Assuming NP$\neq$RP, there is no FPRAS for the partition function of the model when $\lambda > 2\lambda_c$ on above family of hypergraphs .

Towards closing this gap and obtaining a tight transition of approximability, we study the local weak convergence from an infinite sequence of random finite hypergraphs to the infinite uniform regular hypertree with specified symmetry, and prove a surprising result: the existence of such local convergence is fully characterized by the reversibility of the uniform random walk on the infinite hypertree projected on the symmetry classes. We also give explicit constructions sequence of random finite hypergraphs with proper local convergence property when the reversibility condition is satisfied.

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Additional Information

In Campus Calendar
No
Groups

College of Computing, School of Computer Science, ARC

Invited Audience
Undergraduate students, Faculty/Staff, Public, Graduate students
Categories
Seminar/Lecture/Colloquium
Keywords
Algorithm and Randomness Center, ARC, Computational Complexity, Computational Learning Theory, Georgia Tech
Status
  • Created By: Dani Denton
  • Workflow Status: Published
  • Created On: Sep 10, 2015 - 5:47am
  • Last Updated: Apr 13, 2017 - 5:18pm