Anchored Densest Subgraph

Given a graph, densest subgraph search reports a single subgraph that maximizes the density (i.e., average degree). To diversify the search results without imposing rigid constraints, this paper studies the problem of anchored densest subgraph search (ADS). Given a graph, a reference node set S and an anchored node set A with A-R, ADS reports a supergraph of A that maximizes the R-subgraph density ? a density that favors the nodes that are close to S and are not over-popular in comparison with nodes in R. The two levels of localities bring wide applications, as demonstrated by our use cases. For ADS, we propose an algorithm that is local since the complexity is only related to the nodes in S as opposed to the entire graph. Extensive experiments show that our local algorithm for ADS outperforms the global algorithm by up to three orders of magnitudes in time and space consumption; moreover, our local algorithm outperforms existing local community detection solutions in locality, result density, and query processing time and space.