Abstract
We present the first constant-factor approximation algorithms for the following problem: Given a metric space (V,c), a set D ⊆ V of terminals/ customers with demands d:D→ℝ + , a facility opening cost f ∈ ℝ + and a capacity u ∈ ℝ + , find a partition \(D=D_1\dot{\cup}\cdots\dot{\cup} D_k\) and Steiner trees T i for D i (i=1,...,k) with c(E(T i ))+d(D i )≤ u for i=1,...,k such that ∑\(_{i=1}^{k}\) c(E(T i )) + kf is minimum.
This problem arises in VLSI design. It generalizes the bin-packing problem and the Steiner tree problem. In contrast to other network design and facility location problems, it has the additional feature of upper bounds on the service cost that each facility can handle.
Among other results, we obtain a 4.1-approximation in polynomial time, a 4.5-approximation in cubic time and a 5-approximation as fast as computing a minimum spanning tree on (D,c).
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Maßberg, J., Vygen, J. (2005). Approximation Algorithms for Network Design and Facility Location with Service Capacities. In: Chekuri, C., Jansen, K., Rolim, J.D.P., Trevisan, L. (eds) Approximation, Randomization and Combinatorial Optimization. Algorithms and Techniques. APPROX RANDOM 2005 2005. Lecture Notes in Computer Science, vol 3624. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11538462_14
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DOI: https://doi.org/10.1007/11538462_14
Publisher Name: Springer, Berlin, Heidelberg
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