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Subset Sum Problems with Special Digraph Constraints

In: Operations Research Proceedings 2019

Author

Listed:
  • Frank Gurski

    (Institute of Computer Science, Algorithmics for Hard Problems Group)

  • Dominique Komander

    (Institute of Computer Science, Algorithmics for Hard Problems Group)

  • Carolin Rehs

    (Institute of Computer Science, Algorithmics for Hard Problems Group)

Abstract

The subset sum problem is one of the simplest and most fundamental NP-hard problems in combinatorial optimization. We consider two extensions of this problem: The subset sum problem with digraph constraint (SSG) and subset sum problem with weak digraph constraint (SSGW). In both problems there is given a digraph with sizes assigned to the vertices. Within SSG we want to find a subset of vertices whose total size does not exceed a given capacity and which contains a vertex if at least one of its predecessors is part of the solution. Within SSGW we want to find a subset of vertices whose total size does not exceed a given capacity and which contains a vertex if all its predecessors are part of the solution. SSG and SSGW have been introduced by Gourvès et al. who studied their complexity for directed acyclic graphs and oriented trees. We show that both problems are NP-hard even on oriented co-graphs and minimal series-parallel digraphs. Further, we provide pseudo-polynomial solutions for SSG and SSGW with digraph constraints given by directed co-graphs and series-parallel digraphs.

Suggested Citation

  • Frank Gurski & Dominique Komander & Carolin Rehs, 2020. "Subset Sum Problems with Special Digraph Constraints," Operations Research Proceedings, in: Janis S. Neufeld & Udo Buscher & Rainer Lasch & Dominik Möst & Jörn Schönberger (ed.), Operations Research Proceedings 2019, pages 339-346, Springer.
    • Handle: RePEc:spr:oprchp:978-3-030-48439-2_41
    DOI: 10.1007/978-3-030-48439-2_41
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    Cited by:

    1. Steffen Goebbels & Frank Gurski & Dominique Komander, 2022. "The knapsack problem with special neighbor constraints," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 95(1), pages 1-34, February.

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