Fast uniform generation of regular graphs
Theoretical Computer Science
Concentration of non-Lipschitz functions and applications
Random Structures & Algorithms - Probabilistic methods in combinatorial optimization
Generating Random Regular Graphs Quickly
Combinatorics, Probability and Computing
Sampling binary contingency tables with a greedy start
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
State-dependent Importance Sampling and large Deviations
valuetools '06 Proceedings of the 1st international conference on Performance evaluation methodolgies and tools
A Sequential Algorithm for Generating Random Graphs
APPROX '07/RANDOM '07 Proceedings of the 10th International Workshop on Approximation and the 11th International Workshop on Randomization, and Combinatorial Optimization. Algorithms and Techniques
Araneola: A scalable reliable multicast system for dynamic environments
Journal of Parallel and Distributed Computing
Generating random graphs with large girth
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Liftings of tree-structured Markov chains
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Uniform sampling of digraphs with a fixed degree sequence
WG'10 Proceedings of the 36th international conference on Graph-theoretic concepts in computer science
Exact and efficient generation of geometric random variates and random graphs
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
Hi-index | 0.01 |
Random regular graphs play a central role in combinatorics and theoretical computer science. In this paper, we analyze a simple algorithm introduced by Steger and Wormald [9] and prove that it produces an asymptotically uniform random regular graph in a polynomial time. Precisely, for fixed d and n with d=O(n1/3-ε), it is shown that the algorithm generates an asymptotically uniform random d-regular graph on n vertices in time O(nd2). This confirms a conjecture of Wormald. The key ingredient in the proof is a recently developed concentration inequality by the second author.Besides being perhaps the only algorithm which works for relatively large d in practical time, our result also has a significant theoretical value, as it can be used to derive many properties of uniform random regular graphs.