The Maximum Partition Matching

Let S = fC 1 ; C 2 ; : : :; C k g be a collection of pairwise disjoint subsets of U = f1; 2; : : :; ng such that S k i=1 C i = U. A partition matching of S consists of two subsets fa 1 ; a 2 ; : : :; a m g and fb 1 ; b 2 ; : : :; b m g of U together with a sequence of distinct partitions of) such that a i is contained in a subset in the collection A i and b i is contained in a subset in the collection B i for all i = 1; : : :; m. An eecient algorithm is developed that constructs a maximum partition matching for a given collection S. The algorithm can be used to construct optimal parallel routing between two nodes in interconnection networks.