Trees, stars, and multiple biological sequence alignment
SIAM Journal on Applied Mathematics
Mapping the genome: some combinatorial problems arising in molecular biology
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of 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
Efficient approximation algorithms for the Hamming center problem
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
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
More efficient algorithms for closest string and substring problems
RECOMB'08 Proceedings of the 12th annual international conference on Research in computational molecular biology
Finding optimal alignment and consensus of circular strings
CPM'10 Proceedings of the 21st annual conference on Combinatorial pattern matching
A heuristic algorithm based on Lagrangian relaxation for the closest string problem
Computers and Operations Research
Configurations and minority in the string consensus problem
SPIRE'12 Proceedings of the 19th international conference on String Processing and Information Retrieval
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The consensus string problem is finding a representative string (consensus) of a given set $\mathbb{S}$ of strings. In this paper we deal with the consensus string problems optimizing both distance sum and radius, where the distance sum is the sum of (Hamming) distances from the strings in $\mathbb{S}$ to the consensus and the radius is the longest (Hamming) distance from the strings in $\mathbb{S}$ to the consensus. Although there have been results considering either distance sum or radius, there have been no results considering both as far as we know. We present two algorithms to solve the consensus string problems optimizing both distance sum and radius for three strings. The first algorithm finds the optimal consensus string that minimizes both distance sum and radius, and the second algorithm finds the bounded consensus string such that, given constants s and r , the distance sum is at most s and the radius is at most r . Both algorithms take linear time.