January 3rd, Tuesday 12:00, Room 506, Jacobs Building
Title: Exploiting Graph Structure - Beauty and Efficiency in Planar Graphs
Lecturer: Shay Mozes
Lecturer homepage
: http://www.cs.brown.edu/~shay/
Affiliation : Computer Science department, Brown University
In algorithmic graph theory one strives to exploit graph structure to
design efficient algorithms for important, practical problems. In this
talk we make the case for this paradigm by discussing recent progress
in algorithms for fundamental optimization problems in planar graphs,
with applications to basic problems in computer vision known as early
vision tasks. We first discuss nearly linear time algorithms for
computing shortest paths in directed planar graphs with positive and
negative length arcs. We then describe in more detail a nearly linear
time algorithm for finding a maximum single commodity flow in a planar
network with multiple sources and sinks. These algorithms rely on a
host of structural properties of planar graphs, including a beautiful
relation between circulations in a planar graph and shortest paths in
the planar dual of that graph. We conclude with a brief discussion of
distance oracles for planar graphs. No prior knowledge of planar
graphs is assumed.