  Maximal biclique enumeration is a fundamental problem in bipartite graph data
analysis. Existing biclique enumeration methods mainly focus on non-attributed
bipartite graphs and also ignore the \emph{fairness} of graph attributes. In
this paper, we introduce the concept of fairness into the biclique model for
the first time and study the problem of fairness-aware biclique enumeration.
Specifically, we propose two fairness-aware biclique models, called
\nonesidebc~and \ntwosidebc~respectively. To efficiently enumerate all
{\nonesidebc}s, we first present two non-trivial pruning techniques, called
fair $\alpha$-$\beta$ core pruning and colorful fair $\alpha$-$\beta$ core
pruning, to reduce the graph size without losing accuracy. Then, we develop a
branch and bound algorithm, called \onesideFBCEM, to enumerate all single-side
fair bicliques on the reduced bipartite graph. To further improve the
efficiency, we propose an efficient branch and bound algorithm with a
carefully-designed combinatorial enumeration technique. Note that all of our
techniques can also be extended to enumerate all bi-side fair bicliques. We
also extend the two fairness-aware biclique models by constraining the ratio of
the number of vertices of each attribute to the total number of vertices and
present corresponding enumeration algorithms. Extensive experimental results on
five large real-world datasets demonstrate our methods' efficiency,
effectiveness, and scalability.
