On physical mapping algorithms: An error-tolerant test for the consecutive ones property

Abstract

An important problem in physical mapping is to test the consecutive ones property of a (0,1)-matrix: that is, whether it is possible to permute the columns so that each row of the resulting matrix has the ones occur in a consecutive block. This is useful for DNA sequence assembly, for example, in probe hybridization. for cosmid clones and in the STS content mapping of YAC library. The linear time algorithm by Booth and Lueker (1975) for this problem has a serious drawback: the data must be error-free. However, laboratory work is never flawless. We devised a new algorithm for this problem, which has the following advantages:

• 1. conceptually, it is very simple;

• 2. it produces a matrix satisfying the consecutive ones property in linear time when the matrix satisfies the consecutive ones property;

• 3. with reasonable assumptions, it can accommodate the following three types of errors in physical mapping: false negatives, false positives and chimeric clones;

• 4. in the rare case that the assumptions in 3 are not satisfied, our algorithm would suggest additional lab work that could reduce the degree of ambiguity.