Massively Parallel Augmenting Path Algorithms for the Assignment Problem

In this paper we describe how to apply fine grain parallelism to augmenting path algorithms for the dense linear assignment problem. We prove by doing that the technique we suggest, can be efficiently implemented on commercial available, massively parallel computers. Using n processors, our method reduces the computational complexity from the sequential O(n 3 ) to the parallel complexity of O(n 2 ). Exhaustive experiments are performed on a Maspar MP-2 in order to determine which of the algorithmic flavors that fits best onto this kind of architecture. AMS Subject Classifications: 90C08, 65E10 Keywords: Parallel algorithms, matching in bipartite graphs, the assignment problem. 1 Introduction The supercomputers of tomorrow will be parallel computers. Consequently any computational technique for large scale problems has to address the problems of how to parallelize our algorithm. Given the diversity of parallel computers, we also have to identify the most suitable hardware platform..