On Physical Mapping and the consecutive ones property for sparse matrices

On Physical Mapping and the Consecutive Ones Property for Sparse Matrices

A rst step in the investigation of long DNA molecules is often to create a library of clones which are copies of overlapping fragments of the molecule. In creating a clone library the relative order of the clones along the molecule gets lost. Hence, an important problem in molecular biology is to reconstruct this order. This Physical Mapping Problem can be solved using ngerprints of the clones....

On Physical Mapping Algorithms - An Error-Tolerant Test for the Consecutive Ones Property

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 example, in probe hybridization for cosmid clones and in the STS content mapping of YAC library. The linear time algorithm by Booth and L...

A new characterization of matrices with the consecutive ones property

We consider the following constraint satisfaction problem: Given a set F of subsets of a finite set S of cardinality n, and an assignment of intervals of the discrete set {1, . . . , n} to each of the subsets, does there exist a bijection f : S → {1, . . . , n} such that for each element of F, its image under f is same as the interval assigned to it. An interval assignment to a given set of sub...

On the Gapped Consecutive-Ones Property

Motivated by problems of comparative genomics and paleogenomics, we introduce the Gapped Consecutive-Ones Property Problem (k,δ)-C1P: given a binary matrix M and two integers k and δ, can the columns of M be permuted such that each row contains at most k sequences of 1’s and no two consecutive sequences of 1’s are separated by a gap of more than δ 0’s. The classical C1P problem, which is known ...

Consecutive Ones Property