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Title of Journal: J Comb Optim

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Abbravation: Journal of Combinatorial Optimization

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Springer US

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DOI

10.1016/0378-1097(95)00037-6

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1573-2886

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The weighted link ring loading problem

Authors: Qingqin Nong Jinjiang Yuan Yixun Lin
Publish Date: 2008/01/05
Volume: 18, Issue: 1, Pages: 38-50
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Abstract

In the weighted link ring loading problem we are given an nnode undirected ring network Each of its links is associated with a weight Traffic demands are given for each pair of nodes in the ring The load of a link is the sum of the flows routed through the link and the weighted load of a link is the product of its weight and the smallest integer not less than its load The objective of the problem is to find a routing scheme such that the maximum weighted load on the ring is minimized In this paper we consider three variants i demands may be split into two parts and then each part is sent in a different direction ii demands are allowed to be split into two parts but restricted to be integrally split iii each demand must be entirely routed in either of the two directions clockwise or counterclockwise We first prove that the first variant is polynomially solvable We then present a pseudopolynomial time algorithm for the second one Finally for the third one whose NPhardness can be drawn from the result in the literature we derive a polynomialtime approximation scheme PTAS

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