Exact Solutions for Closest String and Related Problems
CLOSEST STRING is one of the core problems in the field of consensus word analysis with particular importance for computational biology. Given k strings of same length and a positive integer d, find a “closest string” s such that none of the given strings has Hamming distance greater than d from s. Closest String is NP-complete. We show how to solve CLOSEST STRING in linear time for constant d (the exponential growth is O(d d . We extend this result to the closely related problems d-MISMATCH and DISTINGUISHING STRING SELECTION. Moreover, we discuss fixed parameter tractability for parameter k and give an efficient linear time algorithm for CLOSEST STRING when k = 3. Finally, the practical usefulness of our findings is substantiated by some experimental results.
KeywordsLinear Time Search Tree Majority Vote Close String Input String
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