On the hardness of counting and sampling center strings.
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 l 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, ‘, 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.).
Department of Computer Science, Colorado State University, 1873 Campus Delivery, Fort Collins, CO 80523-1873, USA. cboucher@cs.colostate.edu
Christina
C
Boucher
Mohamed
M
Omar
D000465:Algorithms; D019295:Computational Biology / Q000379:methods*; D004247:DNA / Q000737:chemistry; D011485:Protein Binding; D011506:Proteins / Q000737:chemistry; D017421:Sequence Analysis / Q000379:methods*
D011506:Proteins; D004247:DNA