Algorithms on strings, trees, and sequences: computer science and computational biology
Algorithms on strings, trees, and sequences: computer science and computational biology
Improved approximation algorithms for tree alignment
Journal of Algorithms
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
The String-to-String Correction Problem
Journal of the ACM (JACM)
The Complexity of Some Problems on Subsequences and Supersequences
Journal of the ACM (JACM)
Topology of strings: median string is NP-complete
Theoretical Computer Science
On the closest string and substring problems
Journal of the ACM (JACM)
Compact Encoding Strategies for DNA Sequence Similarity Search
Proceedings of the Fourth International Conference on Intelligent Systems for Molecular Biology
A PTAS for Distinguishing (Sub)string Selection
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
On the Parameterized Intractability of CLOSEST SUBSTRINGsize and Related Problems
STACS '02 Proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science
Journal of Computer and System Sciences - Special issue on Parameterized computation and complexity
Exact Solutions for Closest String and Related Problems
ISAAC '01 Proceedings of the 12th International Symposium on Algorithms and Computation
Parameterized Complexity
More efficient algorithms for closest string and substring problems
RECOMB'08 Proceedings of the 12th annual international conference on Research in computational molecular biology
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
A three-string approach to the closest string problem
COCOON'10 Proceedings of the 16th annual international conference on Computing and combinatorics
More Efficient Algorithms for Closest String and Substring Problems
SIAM Journal on Computing
A three-string approach to the closest string problem
Journal of Computer and System Sciences
On the closest string via rank distance
CPM'12 Proceedings of the 23rd Annual conference on Combinatorial Pattern Matching
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Given a finite set of strings, the MEDIAN STRING problem consists in finding a string that minimizes the sum of the distances to the strings in the set. Approximations of the median string are used in a very broad range of applications where one needs a representative string that summarizes common information to the strings of the set. It is the case in Classification, in Speech and Pattern Recognition, and in Computational Biology. In the latter, MEDIAN STRING is related to the key problem of Multiple Alignment. In the recent literature, one finds a theorem stating the NP-completeness of the MEDIAN STRING for unbounded alphabets. However, in the above mentioned areas, the alphabet is often finite. Thus, it remains a crucial question whether the MEDIAN STRING problem is NP-complete for finite and even binary alphabets. In this work, we provide an answer to this question and also give the complexity of the related CENTRE STRING problem. Moreover, we study the parametrized complexity of both problems with respect to the number of input strings.