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Multiflow Feasibility: An Annotated Tableau

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Research Trends in Combinatorial Optimization

Summary

We provide a tableau of 189 entries and some annotations presenting the computational complexity of integer multiflow feasibility problems; 21 entries remain open. The tableau is followed by an introduction to the field, providing more problems, reproving some results with new insights, simple proofs, or slight sharpenings motivated by the tableau, paying particular attention to planar (di)graphs with terminals on the boundary. Last, the key-theorems and key-problems of the tableau are listed.

In honor of Bernhard Korte’s 70-th birthday and in memory of the determining impact of the Institut für Diskrete Mathematik, Ökonometrie und Operations Research and its successors on research in the field of Combinatorial Optimization, and in particular on results that have been achieved in the subject of routing, VLSI design, or simply, disjoint paths problems. The second author learnt the subject, proved and wrote down his first results in the subject during his stays in Bonn, had the opportunity to work with students having an excellent training by Professor Korte, and acknowledges gratitude to him for his multiple, generous contribution.

Supported by the Marie Curie Training Network “ADONET” of the European community.

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Authors and Affiliations

  1. Laboratoire G-SCOP, CNRS, INPG, UJF, 46 avenue Félix Viallet, 38031, Grenoble Cedex 1, France

    Guyslain Naves & András Sebő

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  1. Guyslain Naves
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  2. András Sebő
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Editors and Affiliations

  1. Industrial and Systems Engineering, Georgia Tech, 765 Ferst Drive, Atlanta, Georgia, 30332-0205, USA

    William Cook

  2. Institute of Mathematics, Eötvös Loránd University, Pázmány Péter sétány 1/C, H-1117, Budapest, Hungary

    László Lovász

  3. Research Institute for Discrete Mathematics, University of Bonn, Lennéstr. 2, 53113, Bonn, Germany

    Jens Vygen

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Naves, G., Sebő, A. (2009). Multiflow Feasibility: An Annotated Tableau. In: Cook, W., Lovász, L., Vygen, J. (eds) Research Trends in Combinatorial Optimization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-76796-1_12

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