Faster generation of random spanning trees
Name
Kelner-2009-Faster generation of random spanning trees.pdf
Size
294.91 KB
Format
Adobe PDF
Checksum (MD5)
0502a29a3b75b064ebc4399e6b6adae3
Author(s)
Kelner, Jonathan Adam
Madry, Aleksander
Date Issued
March 2010
Journal
50th Annual IEEE Symposium on Foundations of Computer Science, 2009. FOCS '09
Publisher
Institute of Electrical and Electronics Engineers
Citation
Kelner, J.A., and A. Madry. “Faster Generation of Random Spanning Trees.” Foundations of Computer Science, 2009. FOCS '09. 50th Annual IEEE Symposium on. 2009. 13-21. © 2009Institute of Electrical and Electronics Engineers.
Version
Final published version
Abstract
In this paper, we set forth a new algorithm for generating approximately uniformly random spanning trees in undirected graphs. We show how to sample from a distribution that is within a multiplicative (1+ d) of uniform in expected time O[over-(m[sqrt]n log 1/d).This improves the sparse graph case of the best previously known worst-case bound of O(min {mn, n[superscript 2.376]}),which has stood for twenty years. To achieve this goal, we exploit the connection between random walks on graphs and electrical networks, and we use this to introduce a new approach to the problem that integrates discrete random walk-based techniques with continuous linear algebraic methods. We believe that our use of electrical networks and sparse linear system solvers in conjunction with random walks and combinatorial partitioning techniques is a useful paradigm that will find further applications in algorithmic graph theory.
Subjects
spanning trees
random walks on graphs
electrical flows
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1109/FOCS.2009.75
