A branch-and-cut approach to physical mapping of chromosomes by unique end-probes

Thomas Christof, Michael Jünger, John D Kececioglu, Petra Mutzel, Gerhard Reinelt

Research output: Contribution to journalArticle

18 Citations (Scopus)

Abstract

A fundamental problem in computational biology is the construction of physical maps of chromosomes from hybridization experiments between unique probes and clones of chromosome fragments in the presence of error. Alizadeh, Karp, Weisser and Zweig (Algorithmica 13:1/2, 52-76, 1995) first considered a maximum-likelihood model of the problem that is equivalent to finding an ordering of the probes that minimizes a weighted sum of errors and developed several effective heuristics. We show that by exploiting information about the end-probes of clones, this model can be formulated as a Weighted Betweenness Problem. This affords the significant advantage of allowing the well-developed tools of integer linear-programming and branch-and-cut algorithms to be brought to bear on physical mapping, enabling us for the first time to solve small mapping instances to optimality even in the presence of high error. We also show that by combining the optimal solution of many small overlapping Betweenness Problems, one can effectively screen errors from larger instances and solve the edited instance to optimality as a Hamming-Distance Traveling Salesman Problem. This suggests a new approach, a Betweenness-Traveling Salesman hybrid, for constructing physical maps.

Original languageEnglish (US)
Pages (from-to)433-447
Number of pages15
JournalJournal of Computational Biology
Volume4
Issue number4
StatePublished - Dec 1997
Externally publishedYes

Fingerprint

Physical Chromosome Mapping
Branch-and-cut
Chromosomes
Betweenness
Chromosome
Probe
Clone Cells
Linear Programming
Computational Biology
Clone
Optimality
Travelling salesman
Hamming distance
Traveling salesman problem
Integer Linear Programming
Hamming Distance
Travelling salesman problems
Weighted Sums
Linear programming
Maximum likelihood

Keywords

  • Betweenness problem
  • Branch-and-cut
  • Computational biology
  • Linear ordering problem
  • Physical mapping of chromosomes

ASJC Scopus subject areas

  • Molecular Biology
  • Genetics

Cite this

A branch-and-cut approach to physical mapping of chromosomes by unique end-probes. / Christof, Thomas; Jünger, Michael; Kececioglu, John D; Mutzel, Petra; Reinelt, Gerhard.

In: Journal of Computational Biology, Vol. 4, No. 4, 12.1997, p. 433-447.

Research output: Contribution to journalArticle

Christof, T, Jünger, M, Kececioglu, JD, Mutzel, P & Reinelt, G 1997, 'A branch-and-cut approach to physical mapping of chromosomes by unique end-probes', Journal of Computational Biology, vol. 4, no. 4, pp. 433-447.
Christof, Thomas ; Jünger, Michael ; Kececioglu, John D ; Mutzel, Petra ; Reinelt, Gerhard. / A branch-and-cut approach to physical mapping of chromosomes by unique end-probes. In: Journal of Computational Biology. 1997 ; Vol. 4, No. 4. pp. 433-447.
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