Uniform generation of random regular graphs
Abstract
We develop a new approach for uniform generation of combinatorial objects, and apply it to derive a uniform sampler REG for d-regular graphs. REG can be implemented such that each graph is generated in expected time O(nd^3), provided that d=o(n^{1/2}). Our result significantly improves the previously best uniform sampler, which works efficiently only when d=O(n^{1/3}), with essentially the same running time for the same d. We also give a linear-time approximate sampler REG*, which generates a random d-regular graph whose distribution differs from the uniform by o(1) in total variation distance, when d=o(n^{1/2}).
Keywords
Cite
@article{arxiv.1511.01175,
title = {Uniform generation of random regular graphs},
author = {Pu Gao and Nicholas Wormald},
journal= {arXiv preprint arXiv:1511.01175},
year = {2021}
}
Comments
This is a slightly corrected version of the published paper, in which the part of the argument using Lemma 11 had been inadvertently omitted