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Journal of Combinatorial Optimization

, Volume 21, Issue 2, pp 254–267 | Cite as

Approximating capacitated tree-routings in networks

  • Ehab Morsy
  • Hiroshi Nagamochi
Article
  • 72 Downloads

Abstract

Let G=(V,E) be a connected graph such that each edge eE is weighted by a nonnegative real w(e). Let s be a vertex designated as a sink, MV be a set of terminals with a demand function q:MR +, κ>0 be a routing capacity, and λ≥1 be an integer edge capacity. The capacitated tree-routing problem (CTR) asks to find a partition ℳ={Z 1,Z 2,…,Z } of M and a set \({\mathcal{T}}=\{T_{1},T_{2},\ldots,T_{\ell}\}\) of trees of G such that each T i contains Z i ∪{s} and satisfies \(\sum_{v\in Z_{i}}q(v)\leq \kappa\) . A single copy of an edge eE can be shared by at most λ trees in  \({\mathcal{T}}\) ; any integer number of copies of e are allowed to be installed, where the cost of installing a copy of e is w(e). The objective is to find a solution \(({\mathcal{M}},{\mathcal{T}})\) that minimizes the total installing cost. In this paper, we propose a (2+ρ ST )-approximation algorithm to CTR, where ρ ST is any approximation ratio achievable for the Steiner tree problem.

Keywords

Approximation algorithm Graph algorithm Routing problems Network optimization Tree cover 

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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Department of Applied Mathematics and Physics, Graduate School of InformaticsKyoto UniversityKyotoJapan
  2. 2.Department of Mathematics, Faculty of ScienceSuez Canal UniversityIsmailiaEgypt

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