Department of Computer Science | Institute of Theoretical Computer Science | CADMO
Prof. Emo Welzl and Prof. Bernd Gärtner
Mittagsseminar Talk Information |
Date and Time: Thursday, May 17, 2018, 12:15 pm
Duration: 30 minutes
Location: OAT S15/S16/S17
Speaker: Aaron Potechin (KTH Stockholm)
The sum of squares hierarchy is a hierarchy of semidefinite programs which has the three advantages of being broadly applicable (it can be applied whenever the problem can be phrased in terms of polynomial equations over R), powerful (it captures the best known algorithms for several problems including max cut, sparsest cut, and unique games), and in some sense, simple (all it is really using is the fact that squares are non-negative over R). The sum of squares hierarchy can also be viewed as the Positivstellensatz proof system. However, the sum of squares does have a few known weaknesses. One such weakness, as shown by Grigoriev's sum of squares lower bound on the knapsack problem, is that the sum of squares hierarchy is poor at capturing integer arguments. In this talk, we further explore this weakness for symmetric problems. In particular, we describe an analogous sum of squares lower bound for the following Turan type problem: Minimize the number of triangles a graph of a given edge density contains. We then describe the core of the lower bound, which is a simple prover/adversary game, and sketch how this game implies sum of squares lower bounds.
Upcoming talks | All previous talks | Talks by speaker | Upcoming talks in iCal format (beta version!)
Previous talks by year: 2023 2022 2021 2020 2019 2018 2017 2016 2015 2014 2013 2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001 2000 1999 1998 1997 1996
Information for students and suggested topics for student talks
Automatic MiSe System Software Version 1.4803M | admin login