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k-cliques-k-partite-graphs

Description

The algorithm finds all cliques of size k in a k-partite binary undirected graph.

This is an implementation of this paper [@Grunert2002].

Installation

cmake CMakeLists.txt
make

Usage

Run as

./k_cliques_k_partite_graphs --graph_filename path-to-file --max_cliques integer

The parameter --max_cliques d regulates early stopping of the algorithm. When d is non-negative, the algorithm automatically stops when d cliques have been found. Negative values mean no upper bound (default).

If you want to save (and print) all the cliques, add --save_solutions.

Input

The graph file is a simple .txt (specified by --graph_filename) of the following form:

n
p1 p2 ... pn
w11 w12 ... w1n 
...............
wn1 wn2 ... wnn

Here

  1. n is the total number of vertices
  2. pi is the partition of i-th vertex (a number from 1 to k)
  3. wij is the binary weight between vertices i and j.

Note that only the weights for i>j will be used. A connection between two vertices from the same partition will results in an error.

Output

Prints the number of k-cliques. If --save_solutions is specified, the following lines contain each clique in the format

x1 x2 ... xk

with xi being the global index of the vertex in partition i.

Note on other algorithms

I've found only one more algorithm that solves exactly this problem. It is presented in this paper [@Mirghorbani2013]

References

[@Grunert2002]: "Finding all k-cliques in k-partite graphs, an application in textile engineering", Tore Grünert, Stefan Irnich, Hans-Jürgen Zimmermann, Markus Schneider, Burkhard Wulfhorst, Computers & Operations Research (2002), 29: 13. https://doi.org/10.1016/S0305-0548(00)00053-8

[@Mirghorbani2013]: "On finding k-cliques in k-partite graphs" Mirghorbani, M. & Krokhmal, P. Optim Lett (2013) 7: 1155. https://doi.org/10.1007/s11590-012-0536-y