  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.
