Fast Uniform Generation of Random Graphs with Given Degree Sequences

Andrii Arman, Pu Gao, Nicholas Wormald

Research output: Chapter in Book/Report/Conference proceedingConference PaperOther

2 Citations (Scopus)

Abstract

In this paper we provide an algorithm that generates a graph with given degree sequence uniformly at random. Provided that Δ4=O(m), where Δ is the maximal degree and m is the number of edges, the algorithm runs in expected time O(m). Our algorithm significantly improves the previously most efficient uniform sampler, which runs in expected time O(m2Δ2) for the same family of degree sequences. Our method uses a novel ingredient which progressively relaxes restrictions on an object being generated uniformly at random, and we use this to give fast algorithms for uniform sampling of graphs with other degree sequences as well. Using the same method, we also obtain algorithms with expected run time which is (i) linear for power-law degree sequences in cases where the previous best was O(n4.081), and (ii) O(nd+d4) for d-regular graphs when d=o(√ n), where the previous best was O(nd3).

Original languageEnglish
Title of host publicationProceedings - 2019 IEEE 60th Annual Symposium on Foundations of Computer Science, FOCS 2019
Subtitle of host publication60th IEEE Annual Symposium on Foundations of Computer Science, FOCS 2019; Baltimore; United States; 9 November 2019 through 12 November 2019
Place of PublicationPiscataway NJ USA
PublisherIEEE Computer Society
Pages1371-1379
Number of pages9
ISBN (Electronic)9781728149523, 9781728149530
DOIs
Publication statusPublished - 20 Jan 2020
EventIEEE Annual Symposium on Foundations of Computer Science, 2019 - Baltimore, United States of America
Duration: 9 Nov 201912 Nov 2019
Conference number: 60th

Publication series

NameProceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
Volume2019-November
ISSN (Print)0272-5428

Conference

ConferenceIEEE Annual Symposium on Foundations of Computer Science, 2019
Abbreviated titleFOCS 2019
CountryUnited States of America
CityBaltimore
Period9/11/1912/11/19

Keywords

  • Random graphs
  • Switchings
  • Uniform generation

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