On Maximum Weight Clique Algorithms, and How They Are Evaluated

  • Ciaran McCreesh
  • Patrick Prosser
  • Kyle Simpson
  • James TrimbleEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, 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.



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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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Ciaran McCreesh
    • 1
  • Patrick Prosser
    • 1
  • Kyle Simpson
    • 1
  • James Trimble
    • 1
    Email author
  1. 1.University of GlasgowGlasgowScotland

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