Physical Sciences and Mathematics Commons^™

On The Hardness Of Counting And Sampling Center Strings, Christina Boucher, Mohamed Omar

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Given a set S of n strings, each of length ℓ, and a nonnegative value d, we define a center string as a string of length ` that has Hamming distance at most d from each string in S. The #CLOSEST STRING problem aims to determine the number of center strings for a given set of strings S and input parameters n, ℓ, and d. We show #CLOSEST STRING is impossible to solve exactly or even approximately in polynomial time, and that restricting #CLOSEST STRING so that any one of the parameters n, ℓ, or d is fixed leads to …