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

[Clément Canonne]

Reminder: this is *tomorrow morning*. With pastries, and resolution of 
an eight-year old conjecture.

-- Clément

On 10/11/18 1:25 PM, Clément Canonne wrote:
> 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
> 
> -------------------------------
> 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
> 
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