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# Approximating Capacitated Tree-Routings in Networks

• Ehab Morsy
• Hiroshi Nagamochi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4484)

## Abstract

The capacitated tree-routing problem (CTR) in a graph G = (V,E) consists of an edge weight function w:ER  + , a sink s ∈ V, a terminal set M ⊆ V with a demand function q:MR  + , a routing capacity κ> 0, and an integer edge capacity λ ≥ 1. The CTR asks to find a partition $${\cal M}=\{Z_{1},Z_{2},\ldots,Z_{\ell}\}$$ of M and a set $${\cal T}=\{T_{1},T_{2},\ldots,T_{\ell}\}$$ of trees of G such that each T i spans Z i  ∪ {s} and satisfies $$\sum_{v\in Z_{i}}q(v)\leq \kappa$$. A subset of trees in $${\cal T}$$ can pass through a single copy of an edge e ∈ E as long as the number of these trees does not exceed the edge capacity λ; 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 $$({\cal M}, {\cal T})$$ that minimizes the installing cost $$\sum_{e\in E} \lceil |\{T\in {\cal T}\mid T \mbox{ contains }e\}| /\lambda \rceil w(e)$$. In this paper, we propose a $$(2+\rho_{\mbox{\tiny{\sc ST}}})$$-approximation algorithm to the CTR, where $$\rho_{\mbox{\tiny{\sc ST}}}$$ 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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## References

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## Copyright information

© Springer-Verlag Berlin Heidelberg 2007

## Authors and Affiliations

• Ehab Morsy
• 1
• Hiroshi Nagamochi
• 1
1. 1.Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Yoshida Honmachi, Sakyo, Kyoto 606-8501Japan

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