多项式时间的Ramanujan图

2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS) Pub Date : 2016-04-12 DOI:10.1109/FOCS.2016.37

Michael B. Cohen

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引用次数: 48

摘要

Marcus, Spielman和Srivastava最近的工作证明了所有度和所有大小的二部Ramanujan(多)图的存在性。然而，那篇论文并没有提供一个多项式时间算法来实际计算这种图。在这里，我们提供了一个多项式时间算法来计算与此结构相关的某些期望特征多项式。这导致了一个确定性多项式时间算法来计算所有度和所有大小的二部拉马努金(多)图。

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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Ramanujan Graphs in Polynomial Time

Recent work by Marcus, Spielman and Srivastava proves the existence of bipartite Ramanujan (multi) graphs of all degrees and all sizes. However, that paper did not provide a polynomial time algorithm to actually compute such graphs. Here, we provide a polynomial time algorithm to compute certain expected characteristic polynomials related to this construction. This leads to a deterministic polynomial time algorithm to compute bipartite Ramanujan (multi) graphs of all degrees and all sizes.

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来源期刊

2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS)

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