Group-based techniques for identifying top-k degrees in hidden bipartite graphs

Abstract

Graphs are of fundamental importance in modeling data in various domains. Usually, graphs have both their vertices and edges available, which we refer to as explicit graphs. However, in applications such as bioinfomatics, graphs may only have vertices available (e.g., proteins), while the edges are unknown initially (e.g., interactions among proteins), which are called hidden graphs. Thus, the edge probe tests (e.g., biological experiments) are required to detect the presence of edges. This work studies the kMCV (k most connected vertices) problem on a hidden bipartite graph G(B, W) where B and W are two independent vertex sets. The kMCV problem aims to find the top k vertices in B that have the maximum degrees. It has applications in spatial databases, graph databases, and bioinformatics. There is a prior work on the kMCV problem, which is based on the "2-vertex test" model, i.e., an edge probe test can only reveal the existence of an edge between two individual vertices. We study the kMCV problem, in the context of a more general edge probe test model called "group test". A group test can reveal whether there exists some edge between a vertex and a group of vertices. If the group test model is used properly, a single invocation of a group test can reveal as much information as multiple invocations of 2-vertex tests. We discuss the cases and applications where the group test model could be used, and make the following contributions. 1. We propose an algorithm, namely, GMCV, that adaptively leverages the group test model to solve the kMCV problem. 2. We derive cost models for our algorithm GMCV and the prior algorithm. 3. We conduct extensive experiments on both synthetic and real life datasets, and show that our GMCV outperforms the prior algorithm significantly.