Optimal parallel algorithms for b-matchings in trees
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We present adaptive parallel algorithms for b — matchings in trees. The algorithms are designed using the exclusive-read exclusive-write parallel random-access machine (EREW PRAM) model of parallel computation. For a tree of n vertices, the algorithms run in O(n/p+log n) time using p processors (p≤n). When p≤n/(log n), the algorithms are cost optimal.
Ordinary matching problems are special cases of b — matching problems. The best previously known parallel algorithm for ordinary matching in trees runs in O(log n) time using O(n) processors on the EREW PRAM model. Our algorithms achieve the same time complexity with fewer processors.
Keywordsb — matching matching tree parallel algorithm EREW PRAM postorder numbering minimum set cover maximum independent set
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