Abstract
In this paper we devise randomized parallel algorithms which given a unary weighted (di)graphG=(V, E)construct in time O(log2¦ V¦) branchings, perfect matchings, and disjoint cycles of weightexactly k belonging toG. These problems have been studied by Papadimitriou and Yannakakis [PY1], by Barahona and Pulleyblank [BP], by Cameriniet al [CGM], and by Mulmuleyet al. [MVV]. Our algorithms improve previous solutions. Moreover, we give an NC2 algorithm for computing the absolute value of the pfaffian of a skew-symmetric matrix.
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