Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Tuesday, July 17, 2007, 12:15 pm

Duration: This information is not available in the database

Location: OAT S15/S16/S17

Speaker: Tobias Christ

On Dinur's Proof of the PCP Theorem - Part I

In this talk we will give a sketch of Inrit Dinur's new (2005) proof of the PCP theorem with a special focus on how expander graphs are used in her construction. Dinur does not prove the PCP theorem itself, but an equivalent version of it, the NP-hardness of approximating a constraint satisfaction problem given by a constraint graph.

Consider the unsat value of a constraint graph, i.e. the minimal fraction of unsatisfied constraints. We perform a combinatorial transformation of the constraint graph to double the unsat value, while increasing the size of the graph only linearly. The core of this construction is a special notion of graph powering for constraint satisfaction problems. For this "amplification of the gap" to work out, it is crucial that the underlying graph is an expander. So before performing the powering, the graph has to be preprocessed. And since the powering increases the alphabet size of the constraint graph, we have to reduce it again making sure not to lose too much of the unsat value. Repeating the whole procedure logarithmically many times finally gives a new constraint graph in polynomial time, whose unsat value either still is 0 if the original problem was satisfiable or it will be larger than some constant if it was unsatisfiable at the beginning.

Upcoming talks     |     All previous talks     |     Talks by speaker     |     Upcoming talks in iCal format (beta version!)

Previous talks by year:   2024  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