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arXiv · 2105.10094

Finding All Bounded-Length Simple Cycles in a Directed Graph

Anshul Gupta·Toyotaro Suzumura
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Abstract

A new efficient algorithm is presented for finding all simple cycles that satisfy a length constraint in a directed graph. When the number of vertices is non-trivial, most cycle-finding problems are of practical interest for sparse graphs only. We show that for a class of sparse graphs in which the vertex degrees are almost uniform, our algorithm can find all cycles of length less than or equal to $k$ in $O((c+n)(k-1)d^k)$ steps, where $n$ is the number of vertices, $c$ is the total number of cycles discovered, $d$ is the average degree of the graph's vertices, and $k > 1$. While our analysis for the running time addresses only a class of sparse graphs, we provide empirical and experimental evidence of the efficiency of the algorithm for general sparse graphs. This algorithm is a significant improvement over the only other deterministic algorithm for this problem known to us; it also lends itself to massive parallelism. Experimental results of a serial implementation on some large real-world graphs are presented.

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Anshul Gupta, Toyotaro Suzumura. 2021-05-21. Finding All Bounded-Length Simple Cycles in a Directed Graph. https://arxiv.org/abs/2105.10094

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