Efficient algorithms and codes for k-cardinality assignment problems

Given a cost matrix W and a positive integer k, the k-cardinality assignment problem is to assign k rows to k columns so that the sum of the corresponding costs is a minimum. This generalization of the classical assignment problem is solvable in polynomial time, either by transformation to min-cost ow or through speciic algorithms. We consider the algorithm recently proposed by Dell'Amico and Martello for the case where W is dense, and we show how this approach can be used to obtain an eecient algorithm for the case of sparse matrices. Extensive computational experiments show that the resulting code can eeectively solve very large sparse instances and that it is competitive with the previous approach also on dense instances.