Explicit Ramsey Graphs and Two Source Extractors

10/21/2022 11:00 am - 12:00 pm
Benjamin McKenna Fried Tong
CMSA Room G10
Address: CMSA, 20 Garden Street, Cambridge, MA 02138 USA

Speaker: David Zuckerman, Harvard CMSA/University of Texas at Austin

Title: Explicit Ramsey Graphs and Two Source Extractors

Abstract: Ramsey showed that any graph on N nodes contains a clique or independent set of size (log N)/2.  Erdos showed that there exist graphs on N nodes with no clique or independent set of size 2 log N, and asked for an explicit construction of such graphs.  This turns out to relate to the question of extracting high-quality randomness from two independent low-quality sources.  I’ll explain this connection and our recent exponential improvement in constructing two-source extractors.