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Random parallel algorithms for finding exact branchings, perfect matchings, and cycles. (English) Zbl 0827.68052

Summary: We devise randomized parallel algorithms which given a unary weighted (di)graph \(G = (V,E)\) construct in time \(O(\log^2 |V|)\) branchings, perfect matchings, and disjoint cycles of weight exactly \(k\) belonging to \(G\). Our algorithms improve previous solutions. Moreover, we give an \(\text{NC}^2\) algorithm for computing the absolute value of the pfaffian of a skew-symmetric matrix.

MSC:

68W15 Distributed algorithms
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