Learning Heuristics for the Maximum Clique Enumeration Problem Using Low Dimensional Representations

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TAŞDEMİR A. B., Karacan T., Kırmacı E. K., ÖZKAHYA L.

11th International Conference on Computational Data and Social Networks, CSoNet 2022, Virtual, Online, 5 - 07 December 2022, vol.13831 LNCS, pp.236-244 identifier

  • Publication Type: Conference Paper / Full Text
  • Volume: 13831 LNCS
  • Doi Number: 10.1007/978-3-031-26303-3_21
  • City: Virtual, Online
  • Page Numbers: pp.236-244
  • Keywords: Maximum clique enumeration, Node classification, Node embedding
  • Hacettepe University Affiliated: Yes


Approximate solutions to various NP-hard combinatorial optimization problems have been found by learned heuristics using complex learning models. In particular, vertex (node) classification in graphs has been a helpful method towards finding the decision boundary to distinguish vertices in an optimal set from the rest. By following this approach, we use a learning framework for a pruning process of the input graph towards reducing the runtime of the maximum clique enumeration problem. We extensively study the role of using different vertex representations on the performance of this heuristic method, using graph embedding algorithms, such as Node2vec and DeepWalk, and representations using higher-order graph features comprising local subgraph counts. Our results show that Node2Vec and DeepWalk are promising embedding methods in representing nodes towards classification purposes. We observe that using local graph features in the classification process produce more accurate results when combined with a feature elimination process. Finally, we provide tests on random graphs to show the robustness and scalability of our method.