Parametric power supply networks

Shiho Morishita () and Takao Nishizeki ()
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Shiho Morishita: Kwansei Gakuin University
Takao Nishizeki: Kwansei Gakuin University

Journal of Combinatorial Optimization, 2015, vol. 29, issue 1, No 1, 15 pages

Abstract: 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^*

Keywords: Algorithm; Graph; Tree; Parametric network; Power supply (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s10878-013-9661-5

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