拟nc中的二部完美匹配

Proceedings of the forty-eighth annual ACM symposium on Theory of Computing Pub Date : 2016-01-23 DOI:10.1145/2897518.2897564

Stephen A. Fenner, R. Gurjar, T. Thierauf

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引用次数: 77

摘要

我们证明了拟NC2中的二部完美匹配问题。也就是说，它具有准多项式大小为nO(logn)、深度为O(log2n)的一致电路。在此之前，对于这种具有多对数深度的电路，只有一个指数上界是已知的。我们通过对著名的隔离引理的几乎完全非随机化得到了结果，并应用于二部完美匹配问题的有效随机并行算法。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Bipartite perfect matching is in quasi-NC

We show that the bipartite perfect matching problem is in quasi- NC2. That is, it has uniform circuits of quasi-polynomial size nO(logn), and O(log2 n) depth. Previously, only an exponential upper bound was known on the size of such circuits with poly-logarithmic depth. We obtain our result by an almost complete derandomization of the famous Isolation Lemma when applied to yield an efficient randomized parallel algorithm for the bipartite perfect matching problem.

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Proceedings of the forty-eighth annual ACM symposium on Theory of Computing

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