## CompSci 269S, Winter 2008: Theory Seminar

### Feb 15, 2008, in Bren Hall 1423

#
Nondecreasing Paths in a Weighted Graph or: How to Optimally
Read a Train Schedule

## by Virginia Vassilevska, appeared at SODA 2008

## presented by Kevin Wortman

**Abstract:**

A travel booking office has timetables giving arrival and departure
times for all scheduled
trains, including their origins and destinations. A customer presents
a starting city and demands
a route with perhaps several train connections taking him to his
destination as early as possible.
The booking office must find the best route for its customers. This
problem was first considered
in the theory of algorithms by George Minty, who reduced it to a
problem on directed
weighted graphs: find a path from a given source to a given target
such that the consecutive
weights on the path are nondecreasing and the last weight on the path
is minimized. Minty gave
the first algorithm for the single source version of the problem, in
which one finds minimum last
weight nondecreasing paths from the source to every other vertex. In
this paper we give the first
linear time algorithm for this problem. We also define an all pairs
version for the problem and
give a strongly polynomial truly subcubic algorithm for it.