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

__Mittagsseminar Talk Information__ | |

**Date and Time**: Tuesday, June 06, 2017, 12:15 pm

**Duration**: 30 minutes

**Location**: OAT S15/S16/S17

**Speaker**: Mohsen Ghaffari

**(Blackboard Talk)** Improved LOCAL Algorithms for the Lovasz Local Lemma, with Ramifications on LOCAL Complexities

The Lovasz Local Lemma and its algorithmic aspects are certainly not unfamiliar to this crowd. How about LOCAL algorithms for the Lovasz Local Lemma? To my surprise, this topic entails a remarkable significance well beyond a wordplay.

In a very recent revelation, Chang and Pettie [arXiv 1704.06297] showed that any "local" problem that can be solved (randomly) in the LOCAL model in o(log n) rounds on bounded degree graphs can be solved in T_LLL(n) rounds, which denotes the LOCAL round complexity for solving (a relaxed version of) LLL on bounded degree graphs. There was only one problem: the best known bound remained T_LLL(n)=O(log n). But they had a dream! They conjectured that T_LLL(n)=O(log log n).

Making the first step towards their conjecture, and improving significantly on the O(log n)-round LLL algorithm of Chung, Pettie, and Su [2014], we prove that T_LLL(n)=2^{O(sqrt{log log n})}. Hence, any o(log n)-round random LOCAL algorithm for any "local'' problem on bounded degree graphs can be automatically sped up to run in 2^{O(sqrt{log log n})} rounds, that is, e.g., well below O(log^{0.001} n).

This is based on a joint work with Manuela Fischer.

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