An instance I of the Hospitals / Residents problem (HR) involves a set of residents
(graduating medical students) and a set of hospitals, where each hospital has a given
capacity. The residents have preferences for the hospitals, as do hospitals for residents.
A solution of I is a stable matching, which is an assignment of residents to hospitals
that respects the capacity conditions and preference lists in a precise way. In this
paper we present constraint encodings for HR that give rise to important structural
properties. We also present a computational study using both randomly-generated
and real-world instances. Our study suggests that Constraint Programming is indeed
an applicable technology for solving this problem, in terms of both theory and practice
