Uniform generation of random regular graphs of moderate degree
Journal of Algorithms
Algorithms for random generation and counting: a Markov chain approach
Algorithms for random generation and counting: a Markov chain approach
The Markov chain Monte Carlo method: an approach to approximate counting and integration
Approximation algorithms for NP-hard problems
Simple Markov-chain algorithms for generating bipartite graphs and tournaments
Random Structures & Algorithms
Generating random regular graphs
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Generating Random Regular Graphs Quickly
Combinatorics, Probability and Computing
A polynomial-time approximation algorithm for the permanent of a matrix with nonnegative entries
Journal of the ACM (JACM)
Sampling binary contingency tables with a greedy start
Random Structures & Algorithms - Proceedings from the 12th International Conference “Random Structures and Algorithms”, August1-5, 2005, Poznan, Poland
Sampling Regular Graphs and a Peer-to-Peer Network
Combinatorics, Probability and Computing
A Sequential Algorithm for Generating Random Graphs
Algorithmica
Proceedings of the Winter Simulation Conference
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Many applications in network analysis require algorithms to sample uniformly at random from the set of all digraphs with a prescribed degree sequence. We present a Markov chain based approach which converges to the uniform distribution of all realizations. It remains an open challenge whether the Markov chain is rapidly mixing. We also explain in this paper that a popular switching algorithm fails in general to sample uniformly at random because the state graph of the Markov chain decomposes into different isomorphic components. We call degree sequences for which the state graph is strongly connected arc swap sequences. To handle arbitrary degree sequences, we develop two different solutions. The first uses an additional operation (a reorientation of induced directed 3-cycles) which makes the state graph strongly connected, the second selects randomly one of the isomorphic components and samples inside it. Our main contribution is a precise characterization of arc swap sequences, leading to an efficient recognition algorithm. Finally, we point out some interesting consequences for network analysis.