PARALLEL COMPUTATION OF MATCHINGS IN TREES

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, we present an algorithm that determines a maximum cardinality b-matching in O(n/p + log n) time using p processors, where p less-than-or-equal-to n. An algorithm that executes in O(n/p' + log n) time, where 1 < np/(n + p log n) less-than-or-equal-to p' < p less-than-or-equal-to n and p > square-root n/(log n is also designed for the maximum weight b-matching problem in trees. When p less-than-or-equal-to n/(log n), the algorithm are cost-optimal.