Boltzmann Samplers, Pólya Theory, and Cycle Pointing

Details Boltzmann Samplers, Pólya Theory, and Cycle Pointing Boltzmann Samplers, Pólya Theory, and Cycle Pointing

2010-03-23

arxiv.org/abs/1003.4546v2

Computer Science

Discrete Mathematics

41 pages. This is an extended and revised journal version of a conference paper with the title "An unbiased pointing operator

Scientific paper

We introduce a general method to count unlabeled combinatorial structures and to efficiently generate them at random. The approach is based on pointing unlabeled structures in an "unbiased" way that a structure of size n gives rise to n pointed structures. We extend Polya theory to the corresponding pointing operator, and present a random sampling framework based on both the principles of Boltzmann sampling and on P\'olya operators. All previously known unlabeled construction principles for Boltzmann samplers are special cases of our new results. 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 nonplane unrooted trees, and tree-like structures in general, but also to families of graphs (such as cacti graphs and outerplanar graphs) and families of planar maps.

Affiliated with

Also associated with

No associations

Rating

Boltzmann Samplers, Pólya Theory, and Cycle Pointing does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Boltzmann Samplers, Pólya Theory, and Cycle Pointing, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Boltzmann Samplers, Pólya Theory, and Cycle Pointing will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-56502