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Journal of Combinatorial Optimization

, Volume 36, Issue 3, pp 937–964 | Cite as

Subset sum problems with digraph constraints

  • Laurent Gourvès
  • Jérôme MonnotEmail author
  • Lydia Tlilane
Article
  • 109 Downloads

Abstract

We introduce and study optimization problems which are related to the well-known Subset Sum problem. In each new problem, a node-weighted digraph is given and one has to select a subset of vertices whose total weight does not exceed a given budget. Some additional constraints called digraph constraints and maximality need to be satisfied. The digraph constraint imposes that a node must belong to the solution if at least one of its predecessors is in the solution. An alternative of this constraint says that a node must belong to the solution if all its predecessors are in the solution. The maximality constraint ensures that no superset of a feasible solution is also feasible. The combination of these constraints provides four problems. We study their complexity and present some approximation results according to the type of input digraph, such as directed acyclic graphs and oriented trees.

Keywords

Subset sum Maximal problems Digraph constraints Complexity Directed acyclic graphs Oriented trees PTAS 

Notes

Acknowledgements

Many thanks to the anonymous referee and the anonymous associate editor for pertinent and useful comments and suggestions.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Laurent Gourvès
    • 1
  • Jérôme Monnot
    • 1
    Email author
  • Lydia Tlilane
    • 1
  1. 1.CNRS, LAMSADEUniversité Paris-Dauphine, PSL Research UniversityParisFrance

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