  A matching $M$ in a graph $G$ is said to be uniquely restricted if there is
no other matching in $G$ that matches the same set of vertices as $M$. We
describe a polynomial-time algorithm to compute a maximum cardinality uniquely
restricted matching in an interval graph, thereby answering a question of
Golumbic et al. ("Uniquely restricted matchings", M. C. Golumbic, T. Hirst and
M. Lewenstein, Algorithmica, 31:139--154, 2001). Our algorithm actually solves
the more general problem of computing a maximum cardinality "strong independent
set" in an interval nest digraph, which may be of independent interest.
Further, we give linear-time algorithms for computing maximum cardinality
uniquely restricted matchings in proper interval graphs and bipartite
permutation graphs.
