Abstract
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.
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References
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.
K. S. Booth. PQ-Tree Algorithms. PhD thesis, University of California, Berkeley, 1975.
T. Christof. Low-Dimensional 0/1-Polytopes and Branch-and-Cut in Combinatorial Optimization. Aachen: Shaker, 1997.
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.
T. Christof and G. Reinelt. Efficient parallel facet enumeration for 0/1 polytopes. Technical report, University of Heidelberg, Germany, 1997.
T. Christof and G. Reinelt. Algorithmic aspects of using small instance relaxations in parallel branch-and-cut. Technical report, University of Heidelberg, Germany, 1998.
CPLEX. Using the CPLEX Callable Library. CPLEX Optimization, Inc, 1997.
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.
M. Jünger and S. Thienel. The design of the branch-and-cut system ABACUS. Technical Report 95.260, Universität zu Köln, Germany, 1997.
M. Jünger and S. Thienel. Introduction to ABACUS-A Branch-And-CUt system. Technical Report 95.263, Universität zu Köln, Germany, 1997.
S. Leipert. PQ-trees, an implementation as template class in C++. Technical Report 97.259, Universität zu Köln, Germany, 1997.
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.
M. Oswald. PQ-Bäume im Branch & Cut-Ansatz für das Physical-Mapping-Problem mit Endprobes. Master’s thesis, Universität Heidelberg, Germany, 1997.
S. Thienel. ABACUS A Branch-And-CUt System. PhD thesis, Universität zu Köln, 1995.
A. Tucker. A structure theorem for the consecutive 1’s property. Journal of Combinatorial Theory, 12:153–162, 1972.
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Christof, T., Oswald, M., Reinelt, G. (1998). Consecutive Ones and a Betweenness Problem in Computational Biology. In: Bixby, R.E., Boyd, E.A., Ríos-Mercado, R.Z. (eds) Integer Programming and Combinatorial Optimization. IPCO 1998. Lecture Notes in Computer Science, vol 1412. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-69346-7_17
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DOI: https://doi.org/10.1007/3-540-69346-7_17
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