slideshow 3

Complexity seminar

Solving connectivity problems via basic Linear Algebra

Anish Mukherjee
MFF UK

 

Friday, 4. October 2019 - 13:30 to 15:00

in IM, rear building, ground floor

We consider some classical graph connectivity problems like reachability,
shortest path and disjoint paths in this talk. For the first two problems,
we show efficient parallel (dynamic AC^0) algorithms in the dynamic model,
confirming a conjecture of Patnaik and Immerman ’94 for directed
reachability. Recently, we have been able to extend this for batch updates
also. For the optimization version of the disjoint paths problem, we show
efficient sequential and parallel algorithms in planar graphs where all the
terminals lie on a single face. This partly answers an open question of
Colin De Verdière and Schrijver ’08. Interestingly the basic idea behind
these algorithms is to compute some linear algebraic property of the matrix
associated with the given graph, which I shall try to convey in this talk.

Based on joint works with Samir Datta, Raghav Kulkarni, Siddharth Iyer,
Thomas Schwentick, and Thomas Zeume.