Consecutive Ones and a Betweenness Problem in Computational Biology

  • Thomas Christof
  • Marcus Oswald
  • Gerhard Reinelt
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1412)


In this paper we consider a variant of the betweenness prob- lem occurring in computational biology. We present a new polyhedral approach which incorporates the solution of consecutive ones problems and show that it supersedes an earlier one. A particular feature of this new branch-and-cut algorithm is that it is not based on an explicit integer programming formulation of the problem and makes use of automatically generated facet-defining inequalities.


Linear Order Quadratic Assignment Problem Integer Programming Formulation Incidence Vector Cycle Inequality 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    K. Booth and G. Lueker. Testing for the consecutive ones property, interval graphs, and graph planarity using PQ-tree algorithms. Journal of Computer and System Sciences, 13:335–379, 1976.zbMATHMathSciNetGoogle Scholar
  2. 2.
    K. S. Booth. PQ-Tree Algorithms. PhD thesis, University of California, Berkeley, 1975.Google Scholar
  3. 3.
    T. Christof. Low-Dimensional 0/1-Polytopes and Branch-and-Cut in Combinatorial Optimization. Aachen: Shaker, 1997.zbMATHGoogle Scholar
  4. 4.
    T. Christof, M. Jünger, J. Kececioglu, P. Mutzel, and G. Reinelt. A branch-and-cut approach to physical mapping of chromosomes by unique end-probes. Journal of Computational Biology, 4(4):433–447, 1997.CrossRefGoogle Scholar
  5. 5.
    T. Christof and G. Reinelt. Efficient parallel facet enumeration for 0/1 polytopes. Technical report, University of Heidelberg, Germany, 1997.Google Scholar
  6. 6.
    T. Christof and G. Reinelt. Algorithmic aspects of using small instance relaxations in parallel branch-and-cut. Technical report, University of Heidelberg, Germany, 1998.Google Scholar
  7. 7.
    CPLEX. Using the CPLEX Callable Library. CPLEX Optimization, Inc, 1997.Google Scholar
  8. 8.
    M. Jain and E. W. Myers. Algorithms for computing and integrating physical maps using unique probes. In First Annual International Conference on Computational Molecular Biology, pages 84–92. ACM, 1997.Google Scholar
  9. 9.
    M. Jünger and S. Thienel. The design of the branch-and-cut system ABACUS. Technical Report 95.260, Universität zu Köln, Germany, 1997.Google Scholar
  10. 10.
    M. Jünger and S. Thienel. Introduction to ABACUS-A Branch-And-CUt system. Technical Report 95.263, Universität zu Köln, Germany, 1997.Google Scholar
  11. 11.
    S. Leipert. PQ-trees, an implementation as template class in C++. Technical Report 97.259, Universität zu Köln, Germany, 1997.Google Scholar
  12. 12.
    Y. Li, P. M. Pardalos, and M. G. C. Resende. A greedy randomized adaptive search procedure for the quadratic assignment problem. In P. M. Pardalos and H. Wolkowicz, editors, DIMACS Series in Discrete Mathematics and Theoretical Computer Science, Vol. 16, pages 237–261. American Mathematical Society, 1994.Google Scholar
  13. 13.
    M. Oswald. PQ-Bäume im Branch & Cut-Ansatz für das Physical-Mapping-Problem mit Endprobes. Master’s thesis, Universität Heidelberg, Germany, 1997.Google Scholar
  14. 14.
    S. Thienel. ABACUS A Branch-And-CUt System. PhD thesis, Universität zu Köln, 1995.Google Scholar
  15. 15.
    A. Tucker. A structure theorem for the consecutive 1’s property. Journal of Combinatorial Theory, 12:153–162, 1972.zbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Thomas Christof
    • 1
  • Marcus Oswald
    • 1
  • Gerhard Reinelt
    • 1
  1. 1.Institut für Angewandte MathematikUniversität HeidelbergHeidelbergGermany

Personalised recommendations