Approximations and partial solutions for the consensus sequence problem

Abstract

The problem of finding the consensus of a given set of strings is formally defined as follows: given a set of strings S = {s1,...sk}, and a constant d, find, if it exists, a string s*, such that the Hamming distance of s* from each of the strings does not exceed d. In this paper we study an LP relaxation for the problem. We prove an additive upper bound, depending only in the number of strings k, and randomized bounds. We show that empirical results are much better. We also compare our program with some algorithms reported in the literature, and it is shown to perform well. © 2011 Springer-Verlag.