SIAM Journal on Computing
Algorithms on strings, trees, and sequences: computer science and computational biology
Algorithms on strings, trees, and sequences: computer science and computational biology
Distinguishing string selection problems
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
On the closest string and substring problems
Journal of the ACM (JACM)
A Linear-Time Algorithm for the 1-Mismatch Problem
WADS '97 Proceedings of the 5th International Workshop on Algorithms and Data Structures
Banishing Bias from Consensus Sequences
CPM '97 Proceedings of the 8th Annual Symposium on Combinatorial Pattern Matching
Faster algorithms for string matching with k mismatches
Journal of Algorithms - Special issue: SODA 2000
On the Structure of Small Motif Recognition Instances
SPIRE '08 Proceedings of the 15th International Symposium on String Processing and Information Retrieval
Exact Solutions for Closest String and Related Problems
ISAAC '01 Proceedings of the 12th International Symposium on Algorithms and Computation
Introduction to Algorithms, Third Edition
Introduction to Algorithms, Third Edition
More efficient algorithms for closest string and substring problems
RECOMB'08 Proceedings of the 12th annual international conference on Research in computational molecular biology
Hi-index | 5.23 |
Circular strings are different from linear strings in that the last symbol is considered to precede the first symbol. Even though circular strings are biologically important, only a few efforts have been made to solve computational problems on circular strings. In this paper, we introduce consensus problems for circular strings of length n and present the first non-trivial algorithms to find a consensus and an optimal alignment for circular strings by the Hamming distance. They are O(n^2logn)-time algorithms for three circular strings and an O(n^3logn)-time algorithm for four circular strings. Our algorithms are O(n/logn) times faster than the naive algorithms directly using the solutions for the linear consensus problems, which take O(n^3) time for three circular strings and O(n^4) time for four circular strings. This speedup was achieved by reducing the problems into correlations and by formulating and solving systems of linear equations. Moreover, our algorithms use only O(n) space.