Information Complexity and Exact Communication Bounds

Computer Science/Discrete Mathematics Seminar I
Topic:Information Complexity and Exact Communication Bounds
Speaker:Mark Braverman
Affiliation:Princeton University
Date:Monday, December 3
Time/Room:11:15am - 12:15pm/S-101
Video Link:https://video.ias.edu/1213/csdm/MarkBraverman-1203

In this talk we will discuss information complexity -- a measure of the amount of information Alice and Bob need to exchange to solve a problem over distributed inputs. We will present an information-theoretically optimal protocol for computing the AND of two bits distributed between Alice and Bob. We prove that the information complexity of AND is ~1.4923 bits. We use the optimal protocol and its properties to obtain tight bounds for the Disjointness problem, showing that the randomized communication complexity of Disjointness on n bits is ~0.4827n ± o(n). Based on joint work with Ankit Gard, Denis Pankratov, and Omri Weinstein