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On Maximum Weight Clique Algorithms, and How They Are Evaluated

Part of the Lecture Notes in Computer Science book series (LNPSE,volume 10416)


Maximum weight clique and maximum weight independent set solvers are often benchmarked using maximum clique problem instances, with weights allocated to vertices by taking the vertex number mod 200 plus 1. For constraint programming approaches, this rule has clear implications, favouring weight-based rather than degree-based heuristics. We show that similar implications hold for dedicated algorithms, and that additionally, weight distributions affect whether certain inference rules are cost-effective. We look at other families of benchmark instances for the maximum weight clique problem, coming from winner determination problems, graph colouring, and error-correcting codes, and introduce two new families of instances, based upon kidney exchange and the Research Excellence Framework. In each case the weights carry much more interesting structure, and do not in any way resemble the 200 rule. We make these instances available in the hopes of improving the quality of future experiments.


  • Maximum Weight Clique
  • Winner Determination Problem (WDP)
  • Research Excellence Framework
  • Soft Clauses
  • Patient-donor Pairs

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

C. McCreesh, P. Prosser and J. Trimble—This work was supported by the Engineering and Physical Sciences Research Council [grant numbers EP/K503058/1, EP/M508056/1 and EP/P026842/1].

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  1. 1.

    The existing implementation of WLMC does not support the large weights that appear in many of the instances in this paper. Therefore, we could not include this program in our experimental evaluation.

  2. 2.

    It is interesting to note that MWCLQ often resembles Choco but with a higher threshold for switching away from weights, except that sometimes it is worth switching to descending degree as well as ascending degree, and that the three Russian Dolls algorithms exhibit similar heuristic behaviour to each other. We do not understand how ordering heuristics should work with Russian Dolls search, and suggest that this could be a good avenue for future research—for example, perhaps it is better to use different heuristics for different dolls?.

  3. 3.

  4. 4.

    However, in July 2016 Lord Nicholas Stern suggested greater flexibility be allowed.

  5. 5.

    Being a “research-led institution” no papers with a ranking of 1 are allowed.


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The REF instance generator was joint work with David Manlove. We are grateful to David for this, and for helpful discussions on kidney exchange.

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McCreesh, C., Prosser, P., Simpson, K., Trimble, J. (2017). On Maximum Weight Clique Algorithms, and How They Are Evaluated. In: Beck, J. (eds) Principles and Practice of Constraint Programming. CP 2017. Lecture Notes in Computer Science(), vol 10416. Springer, Cham.

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