2026-09-20T08:29:17Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/551262022-01-13T07:54:29Zcom_1721.1_7582com_1721.1_7581col_1721.1_131023
Jonathan A. Kelner.
Ma̧dry, Aleksander
Massachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science.
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
2010-05-25T20:51:00Z
2010-05-25T20:51:00Z
2009
2009
http://hdl.handle.net/1721.1/55126
593873681
Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2009.
Cataloged from PDF version of thesis.
Includes bibliographical references (p. 39-40).
In this thesis, 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+6) of uniform in expected time ... . This improves the sparse graph case of the best previously known worst-case bound of O(min{mn, n2. 376}), which has stood for twenty years. To achieve this goal, we exploit the connection between random walks on graphs and electrical networks 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. This work was done in collaboration with Jonathan Kelner.
by Aleksander Ma̧dry.
S.M.
40 p.
eng
Massachusetts Institute of Technology
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http://dspace.mit.edu/handle/1721.1/7582
Electrical Engineering and Computer Science.
Faster generation of random spanning trees
Thesis
application/pdf
Publication
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<Abstract>In this thesis, 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+6) of uniform in expected time ... . This improves the sparse graph case of the best previously known worst-case bound of O(min{mn, n2. 376}), which has stood for twenty years. To achieve this goal, we exploit the connection between random walks on graphs and electrical networks 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. This work was done in collaboration with Jonathan Kelner.</Abstract>
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