Approximate counting, uniform generation and rapidly mixing Markov chains
Information and Computation
SIAM Journal on Computing
Fast uniform generation of regular graphs
Theoretical Computer Science
A random polynomial-time algorithm for approximating the volume of convex bodies
Journal of the ACM (JACM)
Lifting Markov chains to speed up mixing
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Generating random regular graphs
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
A polynomial-time approximation algorithm for the permanent of a matrix with nonnegative entries
Journal of the ACM (JACM)
Simulated annealing in convex bodies and an O*(n4) volume algorithm
Journal of Computer and System Sciences - Special issue on FOCS 2003
A Sequential Algorithm for Generating Random Graphs
APPROX '07/RANDOM '07 Proceedings of the 10th International Workshop on Approximation and the 11th International Workshop on Randomization, and Combinatorial Optimization. Algorithms and Techniques
The probability that a random multigraph is simple
Combinatorics, Probability and Computing
| Hi-index | 0.00 |
A "lifting" of a Markov chain is a larger chain obtained by replacing each state of the original chain by a set of states, with transition probabilities defined in such a way that the lifted chain projects down exactly to the original one. It is well known that lifting can potentially speed up the mixing time substantially. Essentially all known examples of efficiently implementable liftings have required a high degree of symmetry in the original chain. Addressing an open question of Chen, Lovász and Pak, we present the first example of a successful lifting for a complex Markov chain that has been used in sampling algorithms. This chain, first introduced by Sinclair and Jerrum, samples a leaf uniformly at random in a large tree, given approximate information about the number of leaves in any subtree, and has applications to the theory of approximate counting and to importance sampling in Statistics. Our lifted version of the chain (which, unlike the original one, is non-reversible) gives a significant speedup over the original version whenever the error in the leaf counting estimates is o(1). Our lifting construction, based on flows, is systematic, and we conjecture that it may be applicable to other Markov chains used in sampling algorithms.