FASTEST MIXING MARKOV CHAIN ON GRAPHS WITH SYMMETRIES
Name
Boyd-2009-FASTEST MIXING MARKO.pdf
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338.72 KB
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Checksum (MD5)
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Author(s)
Xiao, Lin
Diaconis, Persi
Boyd, Stephen P.
Parrilo, Pablo A.
Date Issued
June 2009
Journal
SIAM Journal on Scientific Computing
Publisher
Society for Industrial and Applied Mathematics
Citation
Boyd, Stephen et al. “Fastest Mixing Markov Chain on Graphs with Symmetries.” SIAM Journal on Optimization 20.2 (2009): 792-819. © 2009 Society for Industrial and Applied Mathematics
Version
Final published version
Abstract
We show how to exploit symmetries of a graph to efficiently compute the fastest mixing Markov chain on the graph (i.e., find the transition probabilities on the edges to minimize the second-largest eigenvalue modulus of the transition probability matrix). Exploiting symmetry can lead to significant reduction in both the number of variables and the size of matrices in the corresponding semidefinite program, and thus enable numerical solution of large-scale instances that are otherwise computationally infeasible. We obtain analytic or semianalytic results for particular classes of graphs, such as edge-transitive and distance-transitive graphs. We describe two general approaches for symmetry exploitation, based on orbit theory and block-diagonalization, respectively, and establish a formal connection between them.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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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.
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DOI of Published Version
http://dx.doi.org/10.1137/070689413
