Mining Maximal Cliques on Dynamic Graphs Efficiently by Local Strategies

Maximal Clique Enumeration (MCE) is a long standing problem in database community. Though it is extensively studied, almost all researches focus on calculating maximal cliques as a one-time effort. MCE on dynamic graph has been rarely discussed so far, the only work on this topic is to maintain maximal cliques with graph evolving. The key within this problem is to find maximal cliques that contains vertices incident to the inserted edge when edge insertion happens. Up to O(W2) candidates are generated in prior method based on Cartesian product, the overall complexity is O(W2n2) where n, W represents the number of vertices and maximal cliques on the graph. Besides, maximality verification of candidate is conducted frequently by global search. Change of maximal clique induced by graph's updating presents some localities. We propose novel local construction strategy to generate candidates based on linear scan, number of candidates is reduced to O(W), the overall complexity is then reduced to O(Wn2). Furthermore, we present heuristics to reduce the cost incurred by maximality verification. Theoretical analysis and experiments on real graphs indicate that our proposals are effective and efficient.