Abstract
Given a set S of n strings, each of length ℓ, and a non-negative value d, we define a center string as a string of length ℓ that has Hamming distance at most d from each string in S. The #Closest String problem aims to determine the number of unique 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 an FPRAS. We show equivalent results for the problem of efficiently sampling center strings uniformly at random.
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Boucher, C., Omar, M. (2010). On the Hardness of Counting and Sampling Center Strings. In: Chavez, E., Lonardi, S. (eds) String Processing and Information Retrieval. SPIRE 2010. Lecture Notes in Computer Science, vol 6393. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16321-0_12
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DOI: https://doi.org/10.1007/978-3-642-16321-0_12
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