Vertex Orderings to List Triangles faster

Volt is a C++ program to quickly list triangles in a network or graph. The associated paper presents the methods, the available orderings and algorithms, and the experimental results. The NP-hardness proofs are in the file paper_proofs.

Installation & compilation

$ git clone https://github.com/lecfab/volt.git

$ cd volt

$ make

Running

$ ./volt DATASET -o ORDER -a ALGO (more information with $ ./volt --help)

• $ ./volt toygraph.txt to count triangles
• $ ./volt toygraph.txt -t to list triangles
• $ ./volt toygraph.txt -o neigh -a PM to use specific ordering and algorithm

Parameters

• DATASET: an undirected graph representation for nodes [0 to N-1]. It must be a text file where each line corresponds to an edge of the form a b (i.e. a SPACE b, with a and b long unsigned integers). Warning: if DATASET contains loops (a a) or double edges (a b, b a), remove them with $ ./undirect DATASET NEWDATASET.

• -o ORDER: the following orderings are available:

  • split: nodes are split between the beginning and the end of the ordering and sorted by degree
  • check (default): each nodes checks the beginning and end of the ordering and chooses its side
  • neigh (or neighDpm): neighbourhood heuristic to reduce sum d+d-
  • neighDpp): neighbourhood heuristic to reduce sum d+²
  • original: the original order provided by the dataset (warning: it is usually not random)
  • rand: random reordering of nodes
  • deg: sorted by decreasing total degree
  • core: sorted by degeneracy ordering (k-core pealing algorithm)

• -a ALGO: the following algorithms are available to list triangles:

  • PM (default): also called A+- or L+n, it has a complexity sum d+d-
  • PP: also called A++ or S+n, it has complexity sum d+². Note that the equivalent algorithm MM with complexity sum d-² will be applied instead of PP if it takes less time on a given ordered graph
  • comparison: run both A+- and A++ in order to compare their running time

Options

• -t: write triangles in standard output so that they can be saved in a FILE (> FILE) or piped to another PROGRAM (| PROGRAM)
• -e FILE: create a FILE containing the edges of DATASET with the new ordering
• -p P (default 1): use P parallel threads to list triangles. Note that parallelisation may slow down writing if -t is used
• -n N (default 0.01): numeric parameter N used in neigh heuristics. If N=0, the process runs until local minimum is reached; if N>1, the process runs for at most N loops; if 0<N<1, the process runs until improvement threshold N is reached.

Contributors

Copyright © 2022 Fabrice Lécuyer (fabrice.lecuyer@lip6.fr)

This program is free software: you can redistribute it and/or modify it with the same open-source licence (or a later version). It is distributed in the hope that it will be useful, but without any warranty. See the GNU General Public License for more details.