On Density-based Local Community Search

Local community search (LCS) finds a community in a given graph G local to a set R of seed nodes by optimizing an objective function. The objective function f(S) for an induced subgraph S encodes the set inclusion criteria of R to a classic community measurement of S such as the conductance and the density. An ideal algorithm for optimizing f(S) is strongly local, that is, the complexity is dependent on R as opposed to G. This paper formulates a general form of objective functions for LCS using configurations and then focuses on a set C of density-based configurations, each corresponding to a density-based LCS objective function. The paper has two main results. i) A constructive classification of C: a configuration in C has a strongly local algorithm for optimizing its corresponding objective function if and only if it is in CL ⊆ C. ii) A linear programming-based general solution for density-based LCS that is strongly local and practically efficient. This solution is different from the existing strongly local LCS algorithms, which are all based on flow networks.