Back to Basics: Merge Trees

Monday, October 7, 2013 - 2:00pm - 2:50pm
Keller 3-180
Dmitriy Morozov (Lawrence Berkeley Laboratory)
This talk revisits merge trees, a basic topological descriptor that records
connectivity of sublevel sets of a scalar function. We introduce an interleaving
distance between two merge trees and establish its stability to perturbations of
the function. We show that this distance is never smaller than the bottleneck
distance between 0-dimensional persistence diagrams of the function.

On the computational side, we consider a distributed representation of merge
trees that not only improves their parallel computation, but also supports
parallel analysis. As an example, we show how to extract a prescribed levelset
component of the function with minimum communication.
MSC Code: