Random generation of combinatorial structures from a uniform
Theoretical Computer Science
SIAM Journal on Computing
Randomized algorithms
Generating and counting Hamilton cycles in random regular graphs
Journal of Algorithms
Approximately counting Hamilton cycles in dense graphs
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
A polynomial-time approximation algorithm for the permanent of a matrix with nonnegative entries
Journal of the ACM (JACM)
Graph Theory With Applications
Graph Theory With Applications
Accelerating simulated annealing for the permanent and combinatorial counting problems
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Fast approximation of the permanent for very dense problems
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Approximating the permanent: A simple approach
Random Structures & Algorithms
Consecutive ones property and PQ-trees for multisets: Hardness of counting their orderings
Information and Computation
| Hi-index | 5.23 |
We propose an improved algorithm for counting the number of Hamiltonian cycles in a directed graph. The basic idea of the method is sequential acceptance/rejection, which is successfully used in approximating the number of perfect matchings in dense bipartite graphs. As a consequence, a new ratio of the number of Hamiltonian cycles to the number of 1-factors is proposed. Based on this ratio, we prove that our algorithm runs in expected time of O(n^8^.^5) for dense problems. This improves the Markov chain Monte Carlo method, the most powerful existing method, by a factor of at least n^4^.^5(logn)^4 in running time. This class of dense problems is shown to be nontrivial in counting, in the sense that they are #P-Complete.