Sublinear-time parallel algorithms for matching and related problems

The authors present the first sub-linear-time deterministic parallel algorithms for bipartite matching and several related problems, including maximal node-disjoint paths, depth-first search, and flows in zero-one networks. The results are based on a better understanding of the combinatorial structure of the above problems, which lead to new algorithmic techniques. In particular, it is shown how to use maximal matching to extend, in parallel, a current set of node-disjoint paths and how to take advantage of the parallelism that arises when a large number of nodes are active during an execution of a push/relabel network flow algorithm. It is also shown how to apply the techniques to design parallel algorithms for the weighted versions of the above problems.<>