|Computer Science/Discrete Mathematics Seminar I|
|Topic:||Lower bounds for clique vs. independent set|
|Affiliation:||University of Toronto|
|Date:||Monday, February 23|
|Time/Room:||11:15am - 12:15pm/S-101|
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.