An unbiased pointing operator for unlabeled structures, with applications to counting and sampling

Authors:
Manuel Bodirsky;Eric Fusy;Mihyun Kang;Stefan Vigerske
Affiliations:
Humboldt-Universität zu Berlin, Berlin, Germany;INRIA Rocquencourt, Le Chesnay Cedex, France;Humboldt-Universität zu Berlin, Berlin, Germany;Humboldt-Universität zu Berlin, Berlin, Germany
Venue:
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Year:
2007

Citing 3
Cited 2

A calculus for the random generation of labelled combinatorial structures

Theoretical Computer Science
Random Sampling from Boltzmann Principles

ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
Generating Outerplanar Graphs Uniformly at Random

Combinatorics, Probability and Computing

Generating unlabeled connected cubic planar graphs uniformly at random

Random Structures & Algorithms
Asymptotic analysis and random sampling of digitally convex polyominoes

DGCI'13 Proceedings of the 17th IAPR international conference on Discrete Geometry for Computer Imagery

Quantified Score

Hi-index	0.00

Visualization

Abstract

We introduce a general method to count and randomly sample unlabeled combinatorial structures. The approach is based on pointing unlabeled structures in an "unbiased" way, i.e., in such a way that a structure of size n gives rise to n pointed structures. We develop a specific Pólya theory for the corresponding pointing operator, and present a sampling framework relying both on the principles of Boltzmann sampling and on Pólya operators. Our method is illustrated on several examples: in each case, we provide enumerative results and efficient random samplers. The approach applies to unlabeled families of plane and non-plane unrooted trees, and tree-like structures in general, but also to cactus graphs, outerplanar graphs, RNA secondary structures, and classes of planar maps.