The k-cardinality assignment problem

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 M...

Ant System for the k-Cardinality Tree Problem

This paper gives an algorithm for finding the minimum weight tree having k edges in an edge weighted graph. The algorithm combines a search and optimization technique based on pheromone with a weight based greedy local optimization. Experimental results on a large set of problem instances show that this algorithm matches or surpasses other algorithms including an ant colony optimization algorit...

Local Search Algorithms for the k-cardinality Tree Problem

Integer Programming Formulations for the k-Cardinality Tree Problem

In this paper, we present two Integer Programming formulations for the k-Cardinality Tree Problem. The first is a multiflow formulation while the second uses a lifting of the Miller-Tucker-Zemlin constraints. Based on our computational experience, we suggest a two-phase exact solution approach that combines two different solution techniques, each one exploring one of the proposed formulations.

The k-Track Assignment Problem on Partial Orders

The k-track assignment problem is a scheduling problem in which a collection of jobs, represented by intervals, are to be processed by k machines. Two different jobs can be processed by the same machine only if the corresponding intervals do not overlap. We give a compact formulation of the problem and state some polyhedral results for the associated polytope, working in the more general contex...