[theory-seminar] TCS+ talk: Wednesday, October 17, C. Seshadhri, UC Santa Cruz

[Clément Canonne]

Hi everyone,

Next Wednesday, we'll have a TCS+ talk in Gates 463A: we'll be watching 
Sesh (UCSC) talk about a recent result on efficiently finding forbidden 
minors through random walks in graphs (title and abstract below).

it's as usual at 9:55am: come for the breakfast, stay for the 
K_{3,3}-minor finding!

Best,

-- Clément

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Speaker: C. Seshadhri (UC Santa Cruz)
Title: Finding forbidden minors through random walks: (almost) n^{1/2} 
query one-sided testers for minor closed properties

Abstract: Let G be an undirected, bounded degree graph with n vertices. 
Fix a finite graph H, and suppose
one must remove eps*n edges from G to make it H-minor free (for some 
small constant eps > 0). We give a nearly n^{1/2} time algorithm that, 
with high probability, finds an H-minor in such a graph.

As an application, consider a graph G that requires eps*n edge removals 
to make it planar. This result implies an algorithm, with the same 
running time, that produces a K_{3,3} or K_5 minor in G. No prior 
sublinear time bound was known for this problem. By the graph minor 
theorem, we get an analogous result for any minor-closed property.

Up to n^{o(1)} factors, this result resolves a conjecture of 
Benjamini-Schramm-Shapira (STOC 2008) on the existence of one-sided 
property testers for minor-closed properties. Furthermore, our algorithm 
is nearly optimal, by lower bounds of Czumaj et al (RSA 2014).

Joint work with Akash Kumar and Andrew Stolman