Colorado State University

11/13/2008

3:30pm-4:30pm

An "interval graph" is the intersection graph of a set of intervals on a line. That is, there is a vertex for each of the intervals, and two vertices are an edge if the corresponding intervals intersect. Optimization problems on interval graphs, usually motivated by applications to scheduling theory, appear in many undergraduate algorithms texts. Before the structure of DNA was known, interval graphs played a role in establishing its linear topology.

A more recent question arising in genomics is recognizing a "probe interval graph," which as an interval graph where all edges between a given subset of its vertices have been removed. The missing edges represent information about DNA fragments that is unavailable in the laboratory data. We give the first linear time algorithm for the problem. If the graph is a probe interval graph, our algorithm determines the intervals' arrangement on the line.

Much of the talk will be a tutorial on elegant and easy-to-understand results from graph theory, and will conclude with an explanation of how they make the new result possible.

The talk is based on joint work with Yahav Nussbaum of the University of Tel Aviv.

Department of Computer Science

University of Colorado Boulder

Boulder, CO 80309-0430 USA

webmaster@cs.colorado.edu

University of Colorado Boulder

Boulder, CO 80309-0430 USA

webmaster@cs.colorado.edu