Approximating capacitated tree-routings in networks

Ehab Morsy () and Hiroshi Nagamochi ()
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Ehab Morsy: Kyoto University
Hiroshi Nagamochi: Kyoto University

Journal of Combinatorial Optimization, 2011, vol. 21, issue 2, No 7, 254-267

Abstract: Abstract Let G=(V,E) be a connected graph such that each edge e∈E is weighted by a nonnegative real w(e). Let s be a vertex designated as a sink, M⊆V be a set of terminals with a demand function q:M→R +, 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 ℓ } 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 e∈E 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 (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1007/s10878-009-9238-5

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