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arXiv · 2109.09663

Parallel Algorithms for Finding Large Cliques in Sparse Graphs

Lukas Gianinazzi·Maciej Besta·Yannick Schaffner·Torsten Hoefler
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Abstract

We present a parallel k-clique listing algorithm with improved work bounds (for the same depth) in sparse graphs with low degeneracy or arboricity. We achieve this by introducing and analyzing a new pruning criterion for a backtracking search. Our algorithm has better asymptotic performance, especially for larger cliques (when k is not constant), where we avoid the straightforwardly exponential runtime growth with respect to the clique size. In particular, for cliques that are a constant factor smaller than the graph's degeneracy, the work improvement is an exponential factor in the clique size compared to previous results. Moreover, we present a low-depth approximation to the community degeneracy (which can be arbitrarily smaller than the degeneracy). This approximation enables a low depth clique listing algorithm whose runtime is parameterized by the community degeneracy.

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Lukas Gianinazzi, Maciej Besta, Yannick Schaffner, Torsten Hoefler. 2021-09-20. Parallel Algorithms for Finding Large Cliques in Sparse Graphs. https://doi.org/10.1145/3409964.3461800

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