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Parametric power supply networks

Author

Listed:
  • Shiho Morishita

    (Kwansei Gakuin University)

  • Takao Nishizeki

    (Kwansei Gakuin University)

Abstract

Suppose that each vertex of a graph $$G$$ G is either a supply vertex or a demand vertex and is assigned a supply or a demand. All demands and supplies are nonnegative constant numbers in a steady network, while they are functions of a variable $$\lambda $$ λ in a parametric network. Each demand vertex can receive “power” from exactly one supply vertex through edges in $$G$$ G . One thus wishes to partition $$G$$ G to connected components by deleting edges from $$G$$ G so that each component has exactly one supply vertex whose supply is at least the sum of demands in the component. The “partition problem” asks whether $$G$$ G has such a partition. If $$G$$ G has no such partition, one wishes to find the maximum number $$r^*$$ r ∗ , $$0\le r^*

Suggested Citation

  • Shiho Morishita & Takao Nishizeki, 2015. "Parametric power supply networks," Journal of Combinatorial Optimization, Springer, vol. 29(1), pages 1-15, January.
    • Handle: RePEc:spr:jcomop:v:29:y:2015:i:1:d:10.1007_s10878-013-9661-5
    DOI: 10.1007/s10878-013-9661-5
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    References listed on IDEAS

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    1. Edward Minieka, 1972. "Parametric Network Flows," Operations Research, INFORMS, vol. 20(6), pages 1162-1170, December.
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