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We consider the maintenance of maximal bicliques from a dynamic bipartitegraph that changes over time due to the addition or deletion of edges. When theset of edges in a graph changes, we are interested in knowing the change in theset of maximal bicliques (the "change"), rather than in knowing the set ofmaximal bicliques that remain unaffected. The challenge in an efficientalgorithm is to enumerate the change without explicitly enumerating the set ofall maximal bicliques. In this work, we present (1) near-tight bounds on themagnitude of change in the set of maximal bicliques of a graph, due to a changein the edge set (2) a "change-sensitive" algorithm for enumerating the changein the set of maximal bicliques, whose time complexity is proportional to themagnitude of change that actually occurred in the set of maximal bicliques inthe graph. To our knowledge, these are the first algorithms for enumeratingmaximal bicliques in a dynamic graph, with such provable performanceguarantees. Our algorithms are easy to implement, and experimental results showthat their performance exceeds that of current baseline implementations byorders of magnitude.

A Change-Sensitive Algorithm for Maintaining Maximal Bicliques in a Dynamic Bipartite Graph