Improving the Computational Efficiency of the Blitzstein-Diaconis Algorithm for Generating Random Graphs of Prescribed Degree

Abstract

When generating a random graph, if more structure is desired than is given in the popular Erdős-Renyi model, one method is to generate a degree sequence first then create a graph with this degree sequence. Blitzstein and Diaconis[1] (among others) developed a sequential algorithm to create a random graph from a degree sequence. This algorithm is assured to always terminate in a graph with the desired degree sequence; unfortunately, it is slow. This work focuses on the subroutine of the previous algorithm which determines the candidate edges, improving the runtime of the overall algorithm from O(mn 2) to O(mn).

Fast Sequential Creation of Random Realizations of Degree Sequences

“…The second and more serious setback of this approach is that the algorithm’s run-time of O ( mn 2 ) makes it much slower than the MCMC approach. This runtime can be lowered to O ( mn ) time, but this is still significantly slower than the MCMC algorithm [Moseman, 2015]. …”