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Community search over large graphs is a fundamental problem in graphanalysis. Recent studies propose to compute top-k influential communities,where each reported community not only is a cohesive subgraph but also has ahigh influence value. The existing approaches to the problem of top-kinfluential community search can be categorized as index-based algorithms andonline search algorithms without indexes. The index-based algorithms, althoughbeing very efficient in conducting community searches, need to pre-compute aspecial-purpose index and only work for one built-in vertex weight vector. Inthis paper, we investigate on-line search approaches and propose aninstance-optimal algorithm LocalSearch whose time complexity is linearlyproportional to the size of the smallest subgraph that a correct algorithmneeds to access without indexes. In addition, we also propose techniques tomake LocalSearch progressively compute and report the communities in decreasinginfluence value order such that k does not need to be specified. Moreover, weextend our framework to the general case of top-k influential community searchregarding other cohesiveness measures. Extensive empirical studies on realgraphs demonstrate that our algorithms outperform the existing online searchalgorithms by several orders of magnitude.

An Optimal and Progressive Approach to Online Search of Top-k Influential Communities