# Optimal parallel algorithms for b-matchings in trees

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## Abstract

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.

## Keywords

*b*— matching matching tree parallel algorithm EREW PRAM postorder numbering minimum set cover maximum independent set

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