Uniform random posets

We propose a simple algorithm generating labelled posets of given size according to the almost uniform distribution. By "almost uniform" we understand that the distribution of generated posets converges in total variation to the uniform distribution. Our method is based on a Markov chain generating directed acyclic graphs.

[1]  Alan M. Frieze,et al.  Random graphs , 2006, SODA '06.

[2]  Alfred V. Aho,et al.  The Transitive Reduction of a Directed Graph , 1972, SIAM J. Comput..

[3]  W. Trotter,et al.  Combinatorics and Partially Ordered Sets: Dimension Theory , 1992 .

[4]  R. Graham,et al.  Handbook of Combinatorics , 1995 .

[5]  László Babai,et al.  Graph isomorphism in quasipolynomial time [extended abstract] , 2015, STOC.

[6]  Erik Demeulemeester,et al.  RanGen: A Random Network Generator for Activity-on-the-Node Networks , 2003, J. Sched..

[7]  Michael H. Albert,et al.  Random graph orders , 1989 .

[8]  Brendan D. McKay,et al.  Posets on up to 16 Points , 2002, Order.

[9]  László Babai,et al.  Graph isomorphism in quasipolynomial time [extended abstract] , 2016, STOC.

[10]  Tyson R. Browning,et al.  A random generator of resource-constrained multi-project network problems , 2010, J. Sched..

[11]  B. Rothschild,et al.  Asymptotic enumeration of partial orders on a finite set , 1975 .

[12]  M. Mitzenmacher,et al.  Probability and Computing: Chernoff Bounds , 2005 .

[13]  P. Flajolet,et al.  Boltzmann Sampling of Unlabelled Structures , 2006 .

[14]  P. Winkler.  Random orders , 1985 .

[15]  Feller William,et al.  An Introduction To Probability Theory And Its Applications , 1950 .

[16]  Ravi Montenegro,et al.  Mathematical Aspects of Mixing Times in Markov Chains , 2006, Found. Trends Theor. Comput. Sci..

[17]  Elizabeth L. Wilmer,et al.  Markov Chains and Mixing Times , 2008 .

[18]  Mireille Bousquet-Mélou,et al.  Random Generation of Directed Acyclic Graphs , 2001, Electron. Notes Discret. Math..

[19]  William Feller,et al.  An Introduction to Probability Theory and Its Applications , 1967 .

[20]  Peter Winkler,et al.  Connectedness and diameter for random orders of fixed dimension , 1985 .

[21]  Michèle Soria,et al.  Boltzmann sampling of ordered structures , 2009, Electron. Notes Discret. Math..

[22]  Guy Louchard,et al.  Boltzmann Samplers for the Random Generation of Combinatorial Structures , 2004, Combinatorics, Probability and Computing.