Name
Abstract | ||
|---|---|---|
In this paper we provide an algorithm that generates a graph with given degree sequence uniformly at random. Provided that Δ
<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sub>
=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(m
<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup>
Δ
<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup>
) 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(n
<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4.081</sup>
), and (ii) O(nd+d
<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sup>
) for d-regular graphs when d=o(√ n), where the previous best was O(nd
<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup>
). |
Year | DOI | Venue |
|---|---|---|
2019 | 10.1109/FOCS.2019.00084 | 2019 IEEE 60th Annual Symposium on Foundations of Computer Science (FOCS) |
Keywords | Field | DocType |
Uniform generation, random graphs, switchings | Discrete mathematics,Graph,Combinatorics,Random graph,Sampling (statistics),Degree (graph theory),Mathematics | Journal |
Volume | ISSN | ISBN |
abs/1905.03446 | 1523-8288 | 978-1-7281-4953-0 |
Citations | PageRank | References |
0 | 0.34 | 7 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Andrii Arman | 1 | 0 | 2.37 |
| Pu Gao | 2 | 24 | 7.80 |
| Nick Wormald | 3 | 4 | 1.81 |