The complexity of generating an exponentially distributed variate
Journal of Algorithms
LEDA: a platform for combinatorial and geometric computing
LEDA: a platform for combinatorial and geometric computing
Generating random regular graphs
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Fast integer multiplication using modular arithmetic
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Universally utility-maximizing privacy mechanisms
Proceedings of the forty-first annual ACM symposium on Theory of computing
SIAM Journal on Computing
Time bounded random access machines
Journal of Computer and System Sciences
Modern Computer Arithmetic
Efficient generation of networks with given expected degrees
WAW'11 Proceedings of the 8th international conference on Algorithms and models for the web graph
On Buffon machines and numbers
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Are we there yet? when to stop a markov chain while generating random graphs
WAW'12 Proceedings of the 9th international conference on Algorithms and Models for the Web Graph
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The standard algorithm for fast generation of Erdős-Rényi random graphs only works in the Real RAM model. The critical point is the generation of geometric random variates Geo(p), for which there is no algorithm that is both exact and efficient in any bounded precision machine model. For a RAM model with word size w=Ω(loglog(1/p)), we show that this is possible and present an exact algorithm for sampling Geo(p) in optimal expected time $\mathcal{O}(1 + \log(1/p) / w)$. We also give an exact algorithm for sampling min{n, Geo(p)} in optimal expected time $\mathcal{O}(1 + \log(\operatorname{min}\{1/p,n\})/w)$. This yields a new exact algorithm for sampling Erdős-Rényi and Chung-Lu random graphs of n vertices and m (expected) edges in optimal expected runtime $\mathcal{O}(n + m)$ on a RAM with word size w=Θ(logn).