Approximate counting, uniform generation and rapidly mixing Markov chains
Information and Computation
Randomized algorithms
Approximately Counting Hamilton Paths and Cycles in Dense Graphs
SIAM Journal on Computing
The Glauber dynamics on colourings of a graph with high girth and maximum degree
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Finding similar regions in many sequences
Journal of Computer and System Sciences - STOC 1999
Combinatorial Approaches to Finding Subtle Signals in DNA Sequences
Proceedings of the Eighth International Conference on Intelligent Systems for Molecular Biology
Approximate counting by dynamic programming
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
On Counting Independent Sets in Sparse Graphs
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Randomly Colouring Graphs with Lower Bounds on Girth and Maximum Degree
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
A Non-Markovian Coupling for Randomly Sampling Colorings
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
On the complexity of finding common approximate substrings
Theoretical Computer Science
Fast and Practical Algorithms for Planted (l, d) Motif Search
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
| Hi-index | 0.00 |
A set of sequences S is pairwise bounded if the Hamming distance between any pair of sequences in S is at most 2d . The Consensus Sequence problem aims to discern between pairwise bounded sets that have a consensus, and if so, finding one such sequence s *, and those that do not. This problem is closely related to the motif-recognition problem, which abstractly models finding important subsequences in biological data. We give an efficient algorithm for sampling pairwise bounded sets, referred to as MarkovSampling, and show it generates pairwise bounded sets uniformly at random. We illustrate the applicability of MarkovSampling to efficiently solving motif-recognition instances. Computing the expected number of motif sets has been a long-standing open problem in motif-recognition [1,3]. We consider the related problem of counting the number of pairwise bounded sets, give new bounds on number of pairwise bounded sets, and present an algorithmic approach to counting the number of pairwise bounded sets.