On the hardness of counting and sampling center strings

Authors:
Christina Boucher;Mohamed Omar
Affiliations:
David R. Cheriton School of Computer Science, University of Waterloo;Department of Mathematics, University of California, Davis
Venue:
SPIRE'10 Proceedings of the 17th international conference on String processing and information retrieval
Year:
2010

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Abstract

Given a set S of n strings, each of length l, and a non-negative 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 unique 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 an FPRAS. We show equivalent results for the problem of efficiently sampling center strings uniformly at random.