The Maximum Clique problem in graphs asks for a clique of maximum size, a clique being a subset of nodes such that each node is connected to all other nodes of the subset.

As an example, the image above shows a graph of 10 nodes, with a (red) clique of size 4.

You can submit a description of your graph to the Reactive Local Search solver via your World Wide Web browser.
The problem file must be in plain DIMACS format or in binary format; here you can find a converter from ascii Dimacs format to binary format.
If the edge density of the graph is bigger than ~1.2%, the binary storage is more space efficient. So it is preferable to convert an ascii Dimacs file to the binary format before uploading to our server.

The algorithm has been developed by
R. Battiti and M. Protasi.

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• Tutorial and Algorithms Description
• The software corresponds to the description in:
  R. Battiti and M. Protasi. Reactive local search for the maximum clique problem. Algorithmica , April 2001, vol. 29, no. 4, pag. 610--637
  (more recent versions will be available after publication in 2007)
• Interactive Tool

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Define your problem:

• Max Clique problem file:
• Select the CPU time that our machine will dedicate to your problem from the following:
  10 Sec.
  60 Sec.
  600 Sec.