Identifying the most connected vertices in hidden bipartite graphs using group testing

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 ((k)MCV) problem on hidden bipartite graphs, which has applications in spatial databases, graph databases, and bioinformatics. There is a prior work on the (k)MCV 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 (k)MCV 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 (k)MCV problem.