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Exact Solutions for the Steiner Path Cover Problem on Special Graph Classes

In: Operations Research Proceedings 2019

Author

Listed:
  • Frank Gurski

    (Institute of Computer Science)

  • Stefan Hoffmann

    (Institute of Computer Science)

  • Dominique Komander

    (Institute of Computer Science)

  • Carolin Rehs

    (Institute of Computer Science)

  • Jochen Rethmann

    (Faculty of Electrical Engineering and Computer Science)

  • Egon Wanke

    (Institute of Computer Science)

Abstract

The Steiner path problem is a restriction of the well known Steiner tree problem such that the required terminal vertices lie on a path of minimum cost. While a Steiner tree always exists within connected graphs, it is not always possible to find a Steiner path. Despite this, one can ask for the Steiner path cover, i.e. a set of vertex disjoint simple paths which contains all terminal vertices and possibly some of the non-terminal vertices. We show how a Steiner path cover of minimum cardinality for the disjoint union and join composition of two graphs can be computed in linear time from the corresponding values of the involved graphs. The cost of an optimal Steiner path cover is the minimum number of Steiner vertices in a Steiner path cover of minimum cardinality. We compute recursively in linear time the cost within a Steiner path cover for the disjoint union and join composition of two graphs by the costs of the involved graphs. This leads us to a linear time computation of an optimal Steiner path, if it exists, for special co-graphs.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:oprchp:978-3-030-48439-2_40
    DOI: 10.1007/978-3-030-48439-2_40
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    Cited by:

    1. Ante Ćustić & Stefan Lendl, 2022. "The Steiner cycle and path cover problem on interval graphs," Journal of Combinatorial Optimization, Springer, vol. 43(1), pages 226-234, January.
    2. 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.

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