Parallel batch-dynamic graphs: algorithms and lower bounds

In this paper we study the problem of dynamically maintaining graph properties under batches of edge insertions and deletions in the massively parallel model of computation. In this setting, the graph is stored on a number of machines, each having space strongly sublinear with respect to the number of vertices, that is, nε for some constant 0 < ε < 1. Our goal is to handle batches of updates and queries where the data for each batch fits onto one machine in constant rounds of parallel computation, as well as to reduce the total communication between the machines. This objective corresponds to the gradual buildup of databases over time, while the goal of obtaining constant rounds of communication for problems in the static setting has been elusive for problems as simple as undirected graph connectivity.