Abstract
We study the multi-layer crossing minimization problem from a polyhedral point of view. After the introduction of an integer programming formulation of the multi-layer crossing minimization problem, we examine the 2-layer case and derive several classes of facets of the associated polytope. Preliminary computational results for 2- and 3-layer instances indicate, that the usage of the corresponding facet-defining inequalities in a branch-and-cut approach may only lead to a practically useful algorithm, if deeper polyhedral studies are conducted.
Partially supported by DFG-Grant Ju204/7-1, Forschungsschwerpunkt “Effiziente Algorithmen für diskrete Probleme und ihre Anwendungen” and by ESPRIT LTR Project No. 20244 - ALCOM-IT.
Supported in part by NSF grants CCR-9501584 and DMS-9527124.
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Keywords
- Bipartite Graph
- Integer Program
- Short Path Problem
- Integer Programming Formulation
- Crossing Minimization
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Jünger, M., Lee, E.K., Mutzel, P., Odenthal, T. (1997). A polyhedral approach to the multi-layer crossing minimization problem. In: DiBattista, G. (eds) Graph Drawing. GD 1997. Lecture Notes in Computer Science, vol 1353. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63938-1_46
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DOI: https://doi.org/10.1007/3-540-63938-1_46
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