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lp_max_clique's Introduction

Description

Implementation branch and bound algorithm for maximum clique problem in formulation as an continuous nonconvex optimization problem.

Detailed information in this paper: http://www.dcs.gla.ac.uk/~pat/jchoco/clique/indSetMachrahanish/papers/The%20Maximum%20Clique%20Problem.pdf

Instructions

This is Python 3.5.2 realization Required:

  • NetworkX library
  • CPLEX for Python 3.5

To run script you should specify following parameters:

  • --path - path to DIMACS-format graph
  • --time - time limit in seconds

All this graphs are placed in samples folder.
More of them you can find here: http://mat.gsia.cmu.edu/COLOR/instances.html
Huge ones: http://iridia.ulb.ac.be/~fmascia/maximum_clique/DIMACS-benchmark#detC125.9

Results

Graph name #Nodes #Edges Found clique length Time(ms)
MANN_a9.clq 45 918 16 559.974 ms
c-fat200-1.clq 200 1534 12 2488.318 ms
c-fat200-2.clq 200 3235 24 294.705 ms
c-fat500-1.clq 500 4459 14 27029.180 ms
C125.9.clq 125 6963 34 855937.042 ms
c-fat200-5.clq 200 8473 58 10224.952 ms
c-fat500-2.clq 500 9139 26 7544476.644 ms

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