Fast Parallel Algorithms for Edge-Switching to Achieve a Target Visit Rate in Heterogeneous Graphs

An edge switch is an operation on a network (graph) where two edges are selected randomly and one of their end vertices are swapped with each other. Usually, a sequence of these operations are performed to generate network perturbations having the same degree sequence of the original network. Edge switch operations have important applications in graph theory and network analysis, such as in generating random networks with a given degree sequence, modeling and analyzing dynamic networks (e.g., peer-to-peer networks), studying various dynamic phenomena over a network (e.g., disease dynamics over a social contact network). The growth of real-world networks motivates the need to develop efficient parallel algorithms for performing a large sequence of edge switch operations. The dependencies among successive edge switch operations and the requirement of keeping the graph simple (i.e., no self-loops or parallel edges) as the edges are switched lead to significant challenges in designing a parallel algorithm. Addressing these challenges requires complex synchronization and communication among the processors. In this paper, we present a distributed memory parallel algorithm for switching edges in massive networks (networks with billions of edges) and achieve a speedup factor of 85 with 1024 processors. One of the steps in our edge switch algorithm requires the computation of multinomial random variables in parallel. The paper presents the first non-trivial parallel algorithm for the problem. The algorithm achieves a speedup of 925 using 1024 processors.