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

Published

Author(s)

Elizabeth R. Moseman

Abstract

When generating a random graph, if more structure is desired than is given in the popular Erd\H{o}s– Renyi model, one method is to generate a degree sequence first then create a graph with this degree sequence. Blitzstein and Diaconis (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 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(mn2) to O(mn).
Citation
NIST Interagency/Internal Report (NISTIR) - 8066
Report Number
8066

Keywords

random graphs, degree sequence, graph algorithms

Citation

Moseman, E. (2016), Improving the Computational Efficiency of the Blitzstein–Diaconis Algorithm for Generating Random Graphs of Prescribed Degree, NIST Interagency/Internal Report (NISTIR), National Institute of Standards and Technology, Gaithersburg, MD, [online], https://doi.org/10.6028/NIST.IR.8066 (Accessed February 22, 2024)
Created January 6, 2016, Updated November 10, 2018