Recognizing a graph as an interval graph and constructing an interval
representation can be solved in polynomial time.
A natural generalization that arises in several applications is an
additional specification on the length of each interval in the
representation. I will present ongoing work on two problems, namely
drawing an interval graph with specified lenghts on the intervals such
that we minimize the maximum stretch, and the problem of extracting the
largest subgraph that can be drawn with prescribed lengths. This is joint
work with Saurabh Ray.