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

Volume

9

Issue

6

fYear

2012

Firstpage

1843

Lastpage

1846

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;

fLanguage

English

Journal_Title

Computational Biology and Bioinformatics, IEEE/ACM Transactions on

Publisher

ieee

ISSN

1545-5963

Type

jour

DOI

10.1109/TCBB.2012.84

Filename

6205735