## Sublinear-Time Parallel Algorithms for Matching and Related Problems (1988)

Citations: | 33 - 6 self |

### BibTeX

@MISC{Goldberg88sublinear-timeparallel,

author = {Andrew V. Goldberg and Serge A. Plotkin and Pravin M. Vaidya},

title = {Sublinear-Time Parallel Algorithms for Matching and Related Problems},

year = {1988}

}

### Years of Citing Articles

### OpenURL

### Abstract

This paper presents the first sublinear-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. Our results are based on a better understanding of the combinatorial structure of the above problems, which leads to new algorithmic techniques. In particular, we show how to use maximal matching to extend, in parallel, a current set of nodedisjoint 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. We also show how to apply our techniques to design parallel algorithms for the weighted versions of the above problems. In particular, we present sublinear-time deterministic parallel algorithms for finding a minimum-weight bipartite matching and for finding a minimum-cost flow in a network with zero-one capacities, if the weights are polynomially ...