Abstract
Our main result improves the known processor bound by a factor ofn 4 (maintaining the expected parallel running time,O(log3 n)) for the following important problem:find a perfect matching in a general or in a bipartite graph with n vertices. A solution to that problem is used in parallel algorithms for several combinatorial problems, in particular for the problems of finding i) a (perfect) matching of maximum weight, ii) a maximum cardinality matching, iii) a matching of maximum vertex weight, iv) a maximums-t flow in a digraph with unit edge capacities. Consequently the known algorithms for those problems are substantially improved.
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Partially supported by NSF Grants MCS 8303139 and DCR 8511713.
Supporeted by NSF Grants MCS 8203232 and DCR 8507573.
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Galil, Z., Pan, V. Improved processor bounds for combinatorial problems in RNC. Combinatorica 8, 189–200 (1988). https://doi.org/10.1007/BF02122800
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DOI: https://doi.org/10.1007/BF02122800