Computing physical maps of chromosomes with nonoverlapping probes by branch-and-cut

Thomas Christof, John Kececioglu

Research output: Contribution to conferencePaper

7 Scopus citations

Abstract

We introduce a new combinatorial formulation of chromosome physical-mapping by the sampling-without-replacement protocol. In this protocol, which is simple, inexpensive, and has been used to successfully map several organisms, equal-length clones are hybridized against a subset of the clones called probes, which are designed to form a maximal nonoverlapping clone-subset. The output of the protocol is the clone-probe hybridization matrix H. The problem of finding a maximum-likelihood reconstruction of the order of the probes along the chromosome in the presence of false positive and negative hybridization error is equivalent to finding the minimum number of entries of H to change to zeros so that the resulting matrix has at most 2 ones per row, and the consecutive-ones property across rows. This combinatorial problem, which we call 2-Consecutive-Ones Mapping, has a concise integer linear-programming formulation, to which we apply techniques from polyhedral combinatorics. The formulation is unique in that it does not explicitly represent the probe permutation, and in contrast to prior linear-programming approaches, the number of variables is small: in practice, linear in the number of clones. We derive a large class of facet-defining inequalities for the 2-consecutive-ones polytope that we call the augmented k-degree inequalities, and we show that the basic k-degree class can be efficiently separated using bipartite matchings. Computational results with an implementation of the resulting branch-and-cut algorithm applied to both simulated and real data from the complete genome of Aspergillus nidulans show that we can solve many problems to provable optimality and find maps of higher quality than previously possible.

Original languageEnglish (US)
Pages115-123
Number of pages9
StatePublished - Jan 1 1999
Externally publishedYes
EventProceedings of the 1999 3rd Annual International Conference on Computational Molecular Biology, RECOMB '99 - Lyon
Duration: Apr 11 1999Apr 14 1999

Other

OtherProceedings of the 1999 3rd Annual International Conference on Computational Molecular Biology, RECOMB '99
CityLyon
Period4/11/994/14/99

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ASJC Scopus subject areas

  • Computer Science(all)
  • Biochemistry, Genetics and Molecular Biology(all)

Cite this

Christof, T., & Kececioglu, J. (1999). Computing physical maps of chromosomes with nonoverlapping probes by branch-and-cut. 115-123. Paper presented at Proceedings of the 1999 3rd Annual International Conference on Computational Molecular Biology, RECOMB '99, Lyon, .