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

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

Research output: Contribution to journalArticlepeer-review

22 Scopus citations


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
Issue number4
StatePublished - 1997


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

ASJC Scopus subject areas

  • Modeling and Simulation
  • Molecular Biology
  • Genetics
  • Computational Mathematics
  • Computational Theory and Mathematics


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