On the switch Markov chain for perfect matchings
- Submitting institution
-
The University of Leeds
- Unit of assessment
- 11 - Computer Science and Informatics
- Output identifier
- UOA11-1099
- Type
- D - Journal article
- DOI
-
10.1145/2822322
- Title of journal
- Journal of the ACM
- Article number
- 12
- First page
- -
- Volume
- 64
- Issue
- 2
- ISSN
- 0004-5411
- Open access status
- Compliant
- Month of publication
- June
- Year of publication
- 2017
- URL
-
-
- Supplementary information
-
-
- Request cross-referral to
- -
- Output has been delayed by COVID-19
- No
- COVID-19 affected output statement
- -
- Forensic science
- No
- Criminology
- No
- Interdisciplinary
- No
- Number of additional authors
-
2
- Research group(s)
-
A - AC (Algorithms and Complexity)
- Citation count
- 10
- Proposed double-weighted
- No
- Reserve for an output with double weighting
- No
- Additional information
- Randomized counting algorithms were traditionally designed to work for all graphs or classes like degree-bounded graphs. Here we prove that the well-established switch chain efficiently samples perfect matchings uniformly at random in monotone graphs, a class defined by structural properties, and known before under different guises. We utilise the “mountain climbing” problem to prove the mixing time. A preliminary version appeared in the leading conference SODA-2016. The article linked, for the first time, two previously unrelated areas: Markov-chain algorithms and structural graph theory. This work initiated a new stream of research, and led to the EPSRC grants EP/S016562/1, EP/S016694/1.
- Author contribution statement
- -
- Non-English
- No
- English abstract
- -
