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Approximating capacitated tree-routings in networks

Author

Listed:
  • Ehab Morsy

    (Kyoto University
    Suez Canal University)

  • Hiroshi Nagamochi

    (Kyoto University)

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.

Suggested Citation

  • Ehab Morsy & Hiroshi Nagamochi, 2011. "Approximating capacitated tree-routings in networks," Journal of Combinatorial Optimization, Springer, vol. 21(2), pages 254-267, February.
    • Handle: RePEc:spr:jcomop:v:21:y:2011:i:2:d:10.1007_s10878-009-9238-5
    DOI: 10.1007/s10878-009-9238-5
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