Faster random generation of linear extensions

@article{Bubley1998FasterRG,
  title={Faster random generation of linear extensions},
  author={Russ Bubley and Martin E. Dyer},
  journal={Discret. Math.},
  year={1998},
  volume={201},
  pages={81-88}
}
Fast perfect sampling from linear extensions
The Mixing of Markov Chains on Linear Extensions in Practice
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The empirical results suggest that the Markov chain approach to sample linear extensions can be made to scale well in practice, provided that the actual mixing times can be realized by instance-sensitive bounds or termination rules.
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Surveys in Combinatorics, 1999: Random Walks on Combinatorial Objects
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We provide a general framework for computing mixing times of finite Markov chains when its minimal ideal is left zero. Our analysis is based on combining results by Brown and Diaconis with our
Spectral Gap for Random-to-Random Shuffling on Linear Extensions
TLDR
This Markov chain provides a way to sample the linear extensions of the poset with a relaxation time bounded above by n2/(n + 2) and a mixing time of O(n2log n) as for the usual random-to-random shuffling.
Mixing times of lozenge tiling and card shuffling Markov chains
We show how to combine Fourier analysis with coupling arguments to bound the mixing times of a variety of Markov chains. The mixing time is the number of steps a Markov chain takes to approach its
Path coupling: A technique for proving rapid mixing in Markov chains
  • Russ Bubley, M. Dyer
  • Mathematics
    Proceedings 38th Annual Symposium on Foundations of Computer Science
  • 1997
TLDR
A new approach to the coupling technique, which is called path coupling, for bounding mixing rates, is illustrated, which may allow coupling proofs which were previously unknown, or provide significantly better bounds than those obtained using the standard method.
An approximation algorithm for random generation of capacities
TLDR
This paper proposes the 2-layer approximation method, which generates a subset of linear extensions, eliminating those with very low probability, and shows that this method has similar performance compared to the Markov chain but is much less time consuming.
L ∞ -Discrepancy Analysis of Polynomial-Time Deterministic Samplers Emulating Rapidly Mixing Chains
TLDR
A deterministic sampling algorithm based on deterministic random walk, such as the rotor-router model (a.k.a. Propp machine) is proposed, which provides samples with a “distribution” with a point-wise distance at most e from the target distribution, in time polynomial in the input size and e − 1.
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Path coupling: A technique for proving rapid mixing in Markov chains
  • Russ Bubley, M. Dyer
  • Mathematics
    Proceedings 38th Annual Symposium on Foundations of Computer Science
  • 1997
TLDR
A new approach to the coupling technique, which is called path coupling, for bounding mixing rates, is illustrated, which may allow coupling proofs which were previously unknown, or provide significantly better bounds than those obtained using the standard method.
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