Title: Unsupervised Ordering for Maximum Clique
Primary area: learning on graphs and other geometries & topologies
Keywords: Unsupervised Learning, Maximum Clique Problem, Branch-and-Bound (BnB) search, Permutation framework

Abstract: We propose an unsupervised approach for learning vertex orderings for the maximum clique problem by framing it within a permutation-based framework. We transform the combinatorial constraints into geometric relationships such that the ordering of vertices aligns with the clique structures.  By integrating this clique-oriented ordering into branch-and-bound search, we improve search efficiency and reduce the number of computational steps. Our results demonstrate how unsupervised learning of vertex ordering can enhance search efficiency across diverse graph instances. We further study the generalization across different sizes.

TL;DR: Unsupervised learning of clique-oriented vertex orderings improves branch-and-bound search efficiency for the Maximum Clique Problem