Title :
On the Hardness of Counting and Sampling Center Strings
Author :
Boucher, Christina ; Omar, Murad
Author_Institution :
Dept. of Comput. Sci., Colorado State Univ., Fort Collins, CO, USA
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.).
Keywords :
DNA; RNA; biology computing; biomechanics; computational complexity; hardness; molecular biophysics; molecular configurations; polynomial approximation; proteins; sampling methods; #CLOSEST STRING problem; DNA sequences; Hamming distance; RNA sequences; center string counting; center string sampling; computational complexity; fully polynomial-time randomized approximation scheme; hardness; protein sequences; Approximation algorithms; Approximation methods; Bioinformatics; Computational biology; Hamming distance; Polynomials; Sequential analysis; Biological sequence analysis; computational complexity; fully polynomial almost uniform sampler (FPAUS); fully polynomial-time randomized approximation scheme (FPRAS); journal; motif recognition; Algorithms; Computational Biology; DNA; Protein Binding; Proteins; Sequence Analysis;
Journal_Title :
Computational Biology and Bioinformatics, IEEE/ACM Transactions on
DOI :
10.1109/TCBB.2012.84
