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On the Hardness of Counting and Sampling Center Strings
Nov.-Dec. 2012 (vol. 9 no. 6)
pp. 1843-1846
C. Boucher, Dept. of Comput. Sci., Colorado State Univ., Fort Collins, CO, USA
M. Omar, Dept. of Math., California Inst. of Technol., Pasadena, CA, USA
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 a fully polynomial-time randomized approximation scheme (FPRAS). We show equivalent results for the problem of efficiently sampling center strings uniformly at random (u.a.r.).
Index Terms:
sampling methods,biology computing,biomechanics,computational complexity,DNA,hardness,molecular biophysics,molecular configurations,polynomial approximation,proteins,RNA,computational complexity,hardness,center string counting,center string sampling,Hamming distance,#CLOSEST STRING problem,fully polynomial-time randomized approximation scheme,protein sequences,DNA sequences,RNA sequences,Hamming distance,Approximation methods,Polynomials,Approximation algorithms,Bioinformatics,Computational biology,Sequential analysis,computational complexity,Biological sequence analysis,motif recognition,fully polynomial-time randomized approximation scheme (FPRAS),journal,fully polynomial almost uniform sampler (FPAUS)
C. Boucher, M. Omar, "On the Hardness of Counting and Sampling Center Strings," IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol. 9, no. 6, pp. 1843-1846, Nov.-Dec. 2012, doi:10.1109/TCBB.2012.84
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