Learning Computation Bounds for Branch-and-Bound Algorithms to k-plex Extraction

Abstract

k-plex is a representative definition of communities in networks. While the cliques is too stiff to applicate to real cases, the k-plex relaxes the notion of the clique, allowing each node to miss up to k connections. Although k-plexes are more flexible than cliques, finding them is more challenging as their number is greater. In this paper, we aim to detect the k-plex under the size and time constraints, leveraging the new vision of automated learning bounding strategy. We introduce the constraint learning concept to learn the bound strategy from the branch and bound process and develop it into a Mixed Integer Programming framework. While most of the work is dedicated on learn the branch strategy in branch and bound-based algorithms, we focus on the learn to bound strategy which needs to handle the problem that learned strategy might not examine the feasible solution. We adopted the MILP framework and design a set of variables relative to the k-plex property as our constraint space to learn the strategy. The learn to bound strategy learning the original strategy function also reduces the computation load of the bound process to accelerate the branch and bound algorithm. Note that the learn to bound concept can apply to any branch and bound based algorithm with the appropriate framework. We conduct the experiment on different networks, the results show that our learn to branch and bound method does accelerate the original branch and bound method and outperforms other baselines, while also being able to generalize on different graph properties.