  A super-stable matching, which was introduced by Irving, is a solution
concept in a variant of the stable matching problem in which the preferences
may contain ties. Irving proposed a polynomial-time algorithm for the problem
of finding a super-stable matching if a super-stable matching exists. In this
paper, we consider a matroid generalization of a super-stable matching. We call
our generalization of a super-stable matching a super-stable common independent
set. This can be considered as a generalization of the matroid generalization
of a stable matching for strict preferences proposed by Fleiner. We propose a
polynomial-time algorithm for the problem of finding a super-stable common
independent set if a super-stable common independent set exists.
