A data parallel augmenting path algorithm for the dense linear many-to-one assignment problem

The purpose of this study is to describe a data parallel primal-dual augmenting path algorithm for the dense linear many-to-one assignment problem also known as semi-assignment. This problem could for instance be described as assigning n persons to m(n) job groups. The algorithm is tailored speciically for massive SIMD parallelism and employs, in this context, a new eecient breadth-rst-search augmenting path technique which is shown to be faster than the shortest augmenting path search normally used in sequential algorithms for this problem. We show that the best known sequential computational complexity of O(mn 2) for dense problems, is reduced to the parallel complexityof O(mn), on a machine with n processorssupportingreductions in O(1) time. The algorithm is easy to implement eeciently on commercially available massively parallel computers. A range of numerical experiments are performed on a Connection Machine CM200 and a MasPar MP-2. The tests show the good performance of the proposed algorithm.