# Faster random generation of linear extensions

@article{Bubley1998FasterRG, title={Faster random generation of linear extensions}, author={Russ Bubley and M. Dyer}, journal={Discret. Math.}, year={1998}, volume={201}, pages={81-88} }

Abstract This paper examines the problem of sampling (almost) uniformly from the set of linear extensions of a partial order, a classic problem in the theory of approximate sampling. Previous techniques have relied on deep geometric arguments, or have not worked in full generality. Recently, focus has centred on the Karzanov and Khachiyan Markov chain. In this paper, we define a slightly different Markov chain, and present a very simple proof of its rapid mixing, using the method of path… Expand

#### Topics from this paper

#### 175 Citations

The Mixing of Markov Chains on Linear Extensions in Practice

- Mathematics, Computer Science
- IJCAI
- 2017

A Sequential Importance Sampling Algorithm for Counting Linear Extensions

- Computer Science, Mathematics
- ACM J. Exp. Algorithmics
- 2020

Spectral Gap for Random-to-Random Shuffling on Linear Extensions

- Mathematics, Computer Science
- Exp. Math.
- 2017

Path coupling: A technique for proving rapid mixing in Markov chains

- Mathematics, Computer Science
- Proceedings 38th Annual Symposium on Foundations of Computer Science
- 1997

L ∞ -Discrepancy Analysis of Polynomial-Time Deterministic Samplers Emulating Rapidly Mixing Chains

- Computer Science
- COCOON
- 2014

#### References

SHOWING 1-6 OF 6 REFERENCES

The Markov chain Monte Carlo method: an approach to approximate counting and integration

- Computer Science
- 1996

A random polynomial-time algorithm for approximating the volume of convex bodies

- Computer Science
- 1991

On Markov chains f or independent sets, 1997. (Preprint)

- 1997

Counting linear ex tensions.Order

- 1991

Generating linear exten sions fast

- SIAM Journal on Computing
- 1994

Generating a random linear extension o f a partial order.The Annals of Probability

- 1991