Lukáš Poláček: An Information Complexity Approach to Extended Formulations

Lunch is served at 12:00 noon (register at www.doodle.com/sqsx637cva3thmqa ). The presentation starts at *12:10* *pm* (note the time) and ends at 1:00 pm. Those who so wish then reconvene at 1:10 for more technical discussions.

Abstract

Lukáš will present the paper "An Information Complexity Approach to Extended Formulations" by Mark Braverman and Ankur Moitra ( eccc.hpi-web.de/report/2012/131/ ). The abstract of the paper is as follows:

We prove an unconditional lower bound that any linear program that achieves an O(n^{1−\eps}) approximation for clique has size 2^\Omega(n^\eps). There has been considerable recent interest in proving unconditional lower bounds against any linear program. Fiorini et al proved that there is no polynomial sized linear program for traveling salesman. Braun et al proved that there is no polynomial sized O(n^{1/2−\eps})-approximate linear program for clique. Here we prove an optimal and unconditional lower bound against linear programs for clique that matches Håstad's celebrated hardness result. Interestingly, the techniques used to prove such lower bounds have closely followed the progression of techniques used in communication complexity. Here we develop an information theoretic framework to approach these questions, and we use it to prove our main result.

Also we resolve a related question: How many bits of communication are needed to get \eps-advantage over random guessing for disjointness? Kalyanasundaram and Schnitger proved that a protocol that gets constant advantage requires \Omega(n) bits of communication. This result in conjunction with amplification implies that any protocol that gets \eps-advantage requires \Omega(\eps^2 n) bits of communication. Here we improve this bound to \Omega(\eps n), which is optimal for any \eps > 0.