Efficient distributed random walks with applications
Proceedings of the 29th ACM SIGACT-SIGOPS symposium on Principles of distributed computing
An O(log n/ log log n)-approximation algorithm for the asymmetric traveling salesman problem
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Random walks, electric networks and the transience class problem of sandpiles
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
The laplacian paradigm: emerging algorithms for massive graphs
TAMC'10 Proceedings of the 7th annual conference on Theory and Applications of Models of Computation
Chip-firing games, potential theory on graphs, and spanning trees
Journal of Combinatorial Theory Series A
Time hierarchies for sampling distributions
Proceedings of the 4th conference on Innovations in Theoretical Computer Science
Journal of the ACM (JACM)
A simple, combinatorial algorithm for solving SDD systems in nearly-linear time
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
| Hi-index | 0.00 |
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 $(1+\delta)$ of uniform in expected time $\TO(m\sqrt{n}\log 1/\delta)$. This improves the sparse graph case of the best previously known worst-case bound of $O(\min \{mn, n^{2.376}\})$, 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.