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Faster Generation of Random Spanning Trees

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2 Author(s)
Kelner, J.A. ; Massachusetts Inst. of Technol., Cambridge, MA, USA ; Madry, A.

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+ ¿) of uniform in expected time O¿(m¿n log 1/¿). 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, 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.

Published in:

Foundations of Computer Science, 2009. FOCS '09. 50th Annual IEEE Symposium on

Date of Conference:

25-27 Oct. 2009

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