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Triangle Listing Algorithms: Back from the Diversion

机译:三角列表算法:从转移回来

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We show that most algorithms from the literature on listing the triangles of a graph have a common abstraction. Our unifying framework highlights that these seemingly different algorithms are in fact instantiations of a single generic procedure, and even suggests some additional variants. More importantly, it yields parsi-monious implementations that are in general more efficient than those described in the original works. In addition, we show that the running time of nearly every triangle listing variant is in O(a(G)m), where a(G) is the arboricity of the graph and m the number of edges. So far this bound has been proven only for Chiba and Nishizeki's (SIAM J. Computing, 1985) triangle listing algorithm. Finally, algorithmic experimentation reveals that an improved implementation of this algorithm out-performs all subsequently proposed algorithms.
机译:我们展示了列出图形三角形的文献中的大多数算法具有常见的抽象。我们的统一框架突出显示,这些看似不同的算法实际上是单一通用程序的实例化,甚至表明了一些额外的变体。更重要的是,它产生了比原始作品中描述的那一般更有效的解闲实现。此外,我们表明,几乎每个三角形清单变量的运行时间是O(a(g)m),其中a(g)是图形的树突和边的数量。到目前为止,这一界限已被证明是Chiba和Nishizeki的(暹罗J. Computing,1985)三角列表算法。最后,算法实验揭示了这种算法的改进实现,从而执行了所有随后所提出的算法。

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