## The Annals of Probability

- Ann. Probab.
- Volume 19, Number 3 (1991), 1367-1392.

### Generating a Random Linear Extension of a Partial Order

#### Abstract

Given a partial order of $N$ items, a linear extension that is almost uniformly distributed, in the sense of variation distance, is generated. The algorithm runs in polynomial time. The technique used is a coupling for a random walk on a polygonal subset of the unit sphere in $\mathbb{R}^N$. Including is a discussion of how accurately the steps of the random walk must be computed.

#### Article information

**Source**

Ann. Probab., Volume 19, Number 3 (1991), 1367-1392.

**Dates**

First available in Project Euclid: 19 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aop/1176990349

**Digital Object Identifier**

doi:10.1214/aop/1176990349

**Mathematical Reviews number (MathSciNet)**

MR1112421

**Zentralblatt MATH identifier**

0728.60009

**JSTOR**

links.jstor.org

**Subjects**

Primary: 60B10: Convergence of probability measures

Secondary: 60J15 06A10

**Keywords**

Random walk coupling uniform generation volume of a polyhedron

#### Citation

Matthews, Peter. Generating a Random Linear Extension of a Partial Order. Ann. Probab. 19 (1991), no. 3, 1367--1392. doi:10.1214/aop/1176990349. https://projecteuclid.org/euclid.aop/1176990349