Closest string with outliers

On Approximating String Selection Problems with Outliers

Many problems in bioinformatics are about finding strings that approximately represent a collection of given strings. We look at more general problems where some input strings can be classified as outliers. The Close to Most Strings problem is, given a set S of same-length strings, and a parameter d, find a string x that maximizes the number of “non-outliers” within Hamming distance d of x. We ...

A Three-String Approach to the Closest String Problem

Article history: Received 18 May 2010 Received in revised form 11 January 2011 Accepted 21 January 2011 Available online 28 January 2011

Iterative Rounding for the Closest String Problem

The closest string problem is an NP-hard problem, which arises in computational molecular biology and coding theory. Its task is to find a string that minimizes maximum Hamming distance to a given set of strings. This problem can be reduced to an integer program (IP). However, to date, there exists no known polynomial-time algorithm for integer programs. In 2004, Meneses et al. introduced a bra...

Robust iterative closest point algorithm for registration of point sets with outliers

A Closer Look at the Closest String and Closest Substring Problem

Let S be a set of k strings over an alphabet Σ; each string has a length between ` and n. The Closest Substring Problem (CSSP) is to find a minimal integer d (and a corresponding string t of length `) such that each string s ∈ S has a substring of length ` with Hamming distance at most d to t. We say t is the closest substring to S. For ` = n, this problem is known as the Closest String Problem...