Bump hunting in the dark: Local discrepancy maximization on graphs

We study the problem of discrepancy maximization on graphs: given a set of nodes Q of an underlying graph G, we aim to identify a connected subgraph of G that contains many more nodes from Q than other nodes. This variant of the discrepancy-maximization problem extends the well-known notion of “bump hunting” in the Euclidean space. We consider the problem under two access models. In the unrestricted-access model, the whole graph G is given as input, while in the local-access model we can only retrieve the neighbors of a given node in G using a possibly slow and costly interface. We prove that the basic problem of discrepancy maximization on graphs is NP-hard, and empirically evaluate the performance of four heuristics for solving it. For the local-access model we consider three different algorithms that aim to recover a part of G large enough to contain an optimal solution, while using only a small number of calls to the neighbor-function interface. We perform a thorough experimental evaluation in order to understand the trade offs between the proposed methods and their dependencies on characteristics of the input graph.