## 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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### References:

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