## Max Cut is Approximated by Subexponential-Size Linear Programs

*We show that, for every epsilon>0, there is a linear programming relaxation of the Max Cut problem with at most exp(n^epsilon) variables and constraints that achieves approximation ratio at least 1/2 + delta, for some delta(epsilon)>0. Specifically, this is achieved by linear programming relaxations in the Sherali-Adams hierarchy. Previously, the only sub-exponential time algorithms known to approximate Max Cut with an approximation ratio better than 1/2 were based on semidefinite programming or spectral methods. We also provide subexponential time approximation algorithms based on linear programming for Khot's Unique Games problem, which have a qualitatively similar performance to previously known subexponential time algorithms based on spectral methods and on semidefinite programming. Joint work with Sam Hopkins and Tselil Schramm.*

02/12/2019

3:30 pm

Place: viale Regina Elena 295/B, building F, last floor

Luca Trevisan is a professor of Computer Science at Bocconi University. Luca studied at the Sapienza University of Rome, he was a post-doc at MIT and at DIMACS, and he was on the faculty of Columbia University, U.C. Berkeley, and Stanford, before returning to Berkeley in 2014 and, at long last, moving back to Italy in 2019. Luca's research is focused on computational complexity, on analysis of algorithms, and on problems at the intersection of pure mathematics and theoretical computer science. Luca received the STOC'97 Danny Lewin (best student paper) award, the 2000 Oberwolfach Prize, and the 2000 Sloan Fellowship. He was an invited speaker at the 2006 International Congress of Mathematicians. He is a recipient of a 2019 ERC Advanced Grant.