  Given two point sets S and T, in a many-to-many matching between S and T each
point in S is assigned to one or more points in T and vice versa. A
generalization of the many-to-many matching problem is the limited capacity
many-to-many matching problem, where the number of points that can be matched
to each point, that is the capacity of each point, is limited. In this paper,
we provide an O(n^2) time algorithm for the one dimensional minimum-cost
limited capacity many-to-many matching problem, where |S| + |T| = n. Our
algorithm improves the best previous time complexity of O(k(n^2)), that in
which k is the largest capacity of the points in the union of S and T. In this
problem, both S and T lie on the real line and the cost of matching s in S to t
in T is equal to the distance between s and t.
