Lower bounds for clique vs. independent set

Computer Science/Discrete Mathematics Seminar I
Topic:Lower bounds for clique vs. independent set
Speaker:Mika Göös
Affiliation:University of Toronto
Date:Monday, February 23
Time/Room:11:15am - 12:15pm/S-101
Video Link:http://video.ias.edu/csdm/2015/0223-MikaGoos

We prove an $\omega(\log n)$ lower bound on the conondeterministic communication complexity of the Clique vs. Independent Set problem introduced by Yannakakis (STOC 1988, JCSS 1991). As a corollary, this implies superpolynomial lower bounds for the Alon--Saks--Seymour conjecture in graph theory. Our approach is to first exhibit a query complexity separation for the decision tree analogue of the UP vs. coNP question---namely, unambiguous DNF width vs. CNF width---and then "lift" this separation over to communication complexity using a result from prior work.