Identifying the Most Connected Vertices in Hidden Bipartite Graphs Using Group Testing

Abstract

A graph is called hidden if the edges are not explicitly given and edge probe tests are required to detect the presence of edges. This paper studies the k most connected vertices (kMCV) problem on hidden bipartite graphs, which 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 testing” 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 testing.” A group test can reveal whether there exists some edge between a vertex and a group of vertices. If group testing 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 group testing could be used, and present an algorithm, namely, GMCV, that adaptively leverages group testing to solve the kMCV problem.