Faster Generation of Random Spanning Trees

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 + δ) of uniform in expected time O(m √ n log 1/δ). 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. ∗ Research partially supported by NSF grant CCF-0843915. † Research partially supported by Fulb...

• Type: Conference
• Year: 2009
• Where: FOCS
• Authors: Jonathan A. Kelner, Aleksander Madry
• Keywords: Electrical Networks, FOCS 2009, Random Spanning Trees, Random Walks, Theoretical Computer Science