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Computing directed Steiner path covers

Author

Listed:
  • Frank Gurski

    (Heinrich Heine University Düsseldorf)

  • Dominique Komander

    (Heinrich Heine University Düsseldorf)

  • Carolin Rehs

    (Heinrich Heine University Düsseldorf)

  • Jochen Rethmann

    (Niederrhein University of Applied Sciences)

  • Egon Wanke

    (Heinrich Heine University Düsseldorf)

Abstract

In this article we consider the Directed Steiner Path Cover problem on directed co-graphs. Given a directed graph $$G=(V,E)$$ G = ( V , E ) and a set $$T \subseteq V$$ T ⊆ V of so-called terminal vertices, the problem is to find a minimum number of vertex-disjoint simple directed paths, which contain all terminal vertices and a minimum number of non-terminal vertices (Steiner vertices). The primary minimization criteria is the number of paths. We show how to compute in linear time a minimum Steiner path cover for directed co-graphs. This leads to a linear time computation of an optimal directed Steiner path on directed co-graphs, if it exists. Since the Steiner path problem generalizes the Hamiltonian path problem, our results imply the first linear time algorithm for the directed Hamiltonian path problem on directed co-graphs. We also give binary integer programs for the (directed) Hamiltonian path problem, for the (directed) Steiner path problem, and for the (directed) Steiner path cover problem. These integer programs can be used to minimize change-over times in pick-and-place machines used by companies in electronic industry.

Suggested Citation

  • Frank Gurski & Dominique Komander & Carolin Rehs & Jochen Rethmann & Egon Wanke, 2022. "Computing directed Steiner path covers," Journal of Combinatorial Optimization, Springer, vol. 43(2), pages 402-431, March.
    • Handle: RePEc:spr:jcomop:v:43:y:2022:i:2:d:10.1007_s10878-021-00781-7
    DOI: 10.1007/s10878-021-00781-7
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    References listed on IDEAS

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    1. Frank Gurski & Stefan Hoffmann & Dominique Komander & Carolin Rehs & Jochen Rethmann & Egon Wanke, 2020. "Exact Solutions for the Steiner Path Cover Problem on Special Graph Classes," Operations Research Proceedings, in: Janis S. Neufeld & Udo Buscher & Rainer Lasch & Dominik Möst & Jörn Schönberger (ed.), Operations Research Proceedings 2019, pages 331-338, Springer.
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