Fast Sequential Creation of Random Realizations of Degree Sequences

Abstract

We examine the problem of creating random realizations of very large degree sequences. While fast in practice, the Markov chain Monte Carlo (MCMC) method for selecting a realization has limited usefulness for creating large graphs because of memory constraints. Instead, we focus on sequential importance sampling (SIS) schemes for random graph creation. A difficulty with SIS schemes is assuring that they terminate in a reasonable amount of time. We introduce a new sampling method where we guarantee termination while achieving speed comparable to the MCMC method.