Premium
Fast uniform generation of random graphs with given degree sequences
Author(s) -
Arman Andrii,
Gao Pu,
Wormald Nicholas
Publication year - 2021
Publication title -
random structures and algorithms
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.314
H-Index - 69
eISSN - 1098-2418
pISSN - 1042-9832
DOI - 10.1002/rsa.21004
Subject(s) - degree (music) , mathematics , combinatorics , random graph , sequence (biology) , discrete mathematics , algorithm , graph , physics , biology , acoustics , genetics
In this paper we provide an algorithm that generates a graph with given degree sequence uniformly at random. Provided thatΔ 4 = 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 2Δ 2 ) 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 4.081 ), and (ii) O ( nd + d 4 ) for d ‐regular graphs when d = o ( n ) , where the previous best was O ( nd 3 ).