Sublinear-time Parallel Algorithms for Matching and Related Problems
Name
MIT-LCS-TM-357.pdf
Size
6.09 MB
Format
Adobe PDF
Checksum (MD5)
995c1c1480d633c43fd2be28107b4324
Author(s)
Goldberg, Andrew V.
Plotkin, Serge A.
Vaidya, Pravin
Date Issued
June 1988
Series/Report no.
MIT-LCS-TM-357
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 node-disjoint paths and how to take advantage of the parallelism that aries 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 bounded integers.
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