A perfect speedup parallel algorithm for the assignment problem on complete weighted bipartite graphs

The authors present an adaptive parallel algorithm for the assignment problem on complete weighted bipartite graphs, where the edge weights can be real valued and negative. The algorithm is designed using the exclusive-read, exclusive-write parallel random-access machine (EREW PRAM) model of parallel computation. For a complete weighted bipartite graph of n vertices, the algorithm runs in O(n³ /p+n²p) time using p processors. The authors obtain a perfect speedup, with respect to the O(n³) Hungarian method, for p⩽√η, where η is the cardinality of the larger partite set