Triangle Listing Algorithms: Back from the Diversion

Abstract

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 parsimonious 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 outperforms all subsequently proposed algorithms.

DOI: 10.1137/1.9781611973198.1

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Cite this paper

@inproceedings{Ortmann2014TriangleLA, title={Triangle Listing Algorithms: Back from the Diversion}, author={Mark Ortmann and Ulrik Brandes}, booktitle={ALENEX}, year={2014} }