Document Type
Article - postprint
Department
Mathematics (HMC)
Publication Date
2012
Abstract
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.).
Rights Information
© 2012 Christina Boucher and Mohamed Omar
DOI
10.1109/TCBB.2012.84
Recommended Citation
Boucher, Christina and Omar, Mohamed, "On the Hardness of Counting and Sampling Center Strings" (2012). All HMC Faculty Publications and Research. 805.
https://scholarship.claremont.edu/hmc_fac_pub/805
Comments
Final published version can be found at:
Boucher, C.; Omar, M., "On the Hardness of Counting and Sampling Center Strings," Computational Biology and Bioinformatics, IEEE/ACM Transactions on , vol.9, no.6, pp.1843,1846, Nov.-Dec. 2012 doi: 10.1109/TCBB.2012.84