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

TL;DR

This paper introduces a learned heuristic approach for the maximum clique enumeration problem, utilizing low-dimensional graph embeddings and local features to improve pruning efficiency and scalability.

Contribution

It proposes a novel framework combining graph embeddings and local features for vertex classification to enhance maximum clique enumeration efficiency.

Findings

Node2Vec and DeepWalk are effective for vertex classification.

Local graph features improve classification accuracy.

Method demonstrates robustness and scalability on random graphs.

Abstract

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.