Approximate counting: a detailed analysis
BIT - Ellis Horwood series in artificial intelligence
An improved algorithm for transitive closure on acyclic digraphs
Theoretical Computer Science - Thirteenth International Colloquim on Automata, Languages and Programming, Renne
Counting large numbers of events in small registers
Communications of the ACM
On the Distribution of the Transitive Closure in a Random Acyclic Digraph
ESA '93 Proceedings of the First Annual European Symposium on Algorithms
Generalized approximate counting revisited
Theoretical Computer Science
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In this paper we consider the Markov process defined byP1,1=1, Pn,𝓁=(1−λn,𝓁) ·Pn−1,𝓁 +λn,𝓁−1 ·Pn−1,𝓁−1for transition probabilities λn,𝓁=q𝓁 and λn,𝓁=qn−1. We give closed forms for the distributions and the moments of the underlying random variables. Thereby we observe that the distributions can be easily described in terms of q-Stirling numbers of the second kind. Their occurrence in a purely time dependent Markov process allows a natural approximation for these numbers through the normal distribution. We also show that these Markov processes describe some parameters related to the study of random graphs as well as to the analysis of algorithms.