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

Date and Time: Tuesday, October 24, 2017, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Thomas Dueholm Hansen (Aarhus University)

Simulating Branching Programs with Edit Distance and Friends or: A Polylog Shaved is a Lower Bound Made

Backurs and Indyk (STOC'15) recently proved that the Edit Distance of two sequences of equal length cannot be computed in strongly subquadratic time under the Strong Exponential Time Hypothesis (SETH). The result was extended by follow-up works to similar problems such as finding the Longest Common Subsequence (LCS).

SETH is a very strong assumption: it asserts that even linear size CNF formulas cannot be analyzed for satisfiability with an exponential speedup over exhaustive search. We consider much safer assumptions, e.g. that such a speedup is impossible for SAT on much more expressive representations, like subexponential-size NC circuits.

Our main result is a reduction from SAT on Branching Programs to fundamental problems like Edit Distance and LCS. Truly subquadratic algorithms for these problems therefore have consequences that we consider to be far more remarkable than merely faster CNF SAT algorithms. An interesting feature of our work is that even mildly subquadratic algorithms imply new circuit lower bounds. For example, we show that if we can shave an arbitrarily large polylog factor from the complexity of Edit Distance then NEXP does not have non-uniform NC^1 circuits.

Joint work with Amir Abboud, Virginia Vassilevska Williams, and Ryan Williams.

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