NDLI: Boltzmann Samplers, Plya Theory, and Cycle Pointing

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Fusy, ric Vigerske, Stefan Kang, Mihyun Bodirsky, Manuel
Copyright Year	2011
Abstract	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 so that a structure of size n gives rise to n pointed structures. We extend Plya theory to the corresponding pointing operator and present a random sampling framework based on both the principles of Boltzmann sampling and Plya operators. All previously known unlabeled construction principles for Boltzmann samplers are special cases of our new results. Our method is illustrated in 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.
Starting Page	721
Ending Page	769
Page Count	49
File Format	PDF
ISSN	00975397
DOI	10.1137/100790082
e-ISSN	10957111
Journal	SIAM Journal on Computing (SMJCAT)
Issue Number	3 (Special Section on Foundations of Computer Science)
Volume Number	40
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2011-06-09
Access Restriction	Subscribed
Subject Keyword	Plya theory graphs Enumeration in graph theory random generation maps Exact enumeration problems, generating functions unlabeled enumeration Boltzmann trees Power series Asymptotic enumeration
Content Type	Text
Resource Type	Article
Subject	Mathematics Computer Science

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in