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
Finding similar regions in many strings
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Distinguishing string selection problems
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Faster algorithms for string matching with k mismatches
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
On the closest string and substring problems
Journal of the ACM (JACM)
Introduction to Algorithms
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
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
Consensus Optimizing Both Distance Sum and Radius
SPIRE '09 Proceedings of the 16th International Symposium on String Processing and Information Retrieval
More efficient algorithms for closest string and substring problems
RECOMB'08 Proceedings of the 12th annual international conference on Research in computational molecular biology
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We consider the problem of finding the optimal alignment and consensus (string) of circular strings. Circular strings are different from linear strings in that the first (leftmost) symbol of a circular string is wrapped around next to the last (rightmost) symbol. In nature, for example, bacterial and mitochondrial DNAs typically form circular strings. The consensus string problem is finding a representative string (consensus) of a given set of strings, and it has been studied on linear strings extensively. However, only a few efforts have been made for the consensus problem for circular strings, even though circular strings are biologically important. In this paper, we introduce the consensus problem for circular strings and present novel algorithms to find the optimal alignment and consensus of circular strings under the Hamming distance metric. They are O(n2 log n)-time algorithms for three circular strings and an O(n3 log n)-time algorithm for four circular strings. Our algorithms are O(n/ log n) times faster than the naïve algorithm directly using the solutions for the linear consensus problems, which takes O(n3) time for three circular strings and O(n4) time for four circular strings. We achieved this speedup by adopting a convolution and a system of linear equations into our algorithms to reflect the characteristics of circular strings that we found.