almost-optimum speed-ups of algorithms for bipartite matching and related problems
We present algorithms for matching and related problems that run on an EREW PRAM with p processors. Given is a bipartite graph G with n vertices, m edges, and integral edge costs at most N in magnitude. We give an algorithm for the assignment problem (minimum cost perfect bipartite matching) that runs in &Ogr; (? nm log ( nN )(log(2 p ))/ p ) time and &Ogr; ( m ) space, for p ? m /(? n log 2 n ). For p = 1 this improves the best known sequential algorithm, and is within a factor of log ( nN ) of the best known bound for the problem without costs (maximum cardinality matching). For p > 1 the time is within a factor of log p of optimum speed-up. Extensions include an algorithm for maximum cardinality bipartite matching with slightly better processor bounds, and similar results for bipartite degree-constrained subgraph problems (with and without costs). Our ideas also extend to general graph matching problems.
algorithm matching processor bipartite graph integrability cost assignment log timing space factor extensibility general graph matching