Article

Hardness of Buy-at-Bulk Network Design

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Matthew AndrewsAuthors Info & Claims

FOCS '04: Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science

Pages 115 - 124

https://doi.org/10.1109/FOCS.2004.32

Published: 17 October 2004 Publication History

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Abstract

We consider the Buy-at-Bulk network design problem in which we wish to design a network for carrying multicommodity demands from a set of source nodes to a set of destination nodes. The key feature of the problem is that the cost of capacity on each edge is concave and hence exhibits economies of scale. If the cost of capacity per unit length can be different on different edges then we say that the problem is non-uniform. The problem is uniform otherwise. We show that for any constant, if NP ZIPTIME(n^polylog n) then there is no 0(\log ^{\frac{1}{2} - \gamma } N)-approximation algorithm for non-uniform Buy-at-Bulk network design and there is no 0(\log ^{\frac{1}{4} - \gamma } N)-approximation algorithm for the uniform problem.

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Zhang YZhang HCong PWang W(2024)ROND: Rethinking Overlay Network Design with Underlay Network AwarenessProceedings of the ACM on Networking10.1145/36562982:CoNEXT2(1-22)Online publication date: 13-Jun-2024
https://dl.acm.org/doi/10.1145/3656298
Emek YKutten SLavi RShi Y(2020)Approximating Generalized Network Design under (Dis)economies of Scale with Applications to Energy EfficiencyJournal of the ACM10.1145/337738767:1(1-33)Online publication date: 7-Feb-2020
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Friedrichs SLenzen C(2018)Parallel Metric Tree Embedding Based on an Algebraic View on Moore-Bellman-FordJournal of the ACM10.1145/323159165:6(1-55)Online publication date: 22-Nov-2018
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Hardness of Buy-at-Bulk Network Design
1. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory
  2. Mathematical analysis
    1. Functional analysis
2. Theory of computation
  1. Design and analysis of algorithms
    1. Graph algorithms analysis

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FOCS '04: Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science

October 2004

609 pages

ISBN:0769522289

Publisher

IEEE Computer Society

United States

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Published: 17 October 2004

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Zhang YZhang HCong PWang W(2024)ROND: Rethinking Overlay Network Design with Underlay Network AwarenessProceedings of the ACM on Networking10.1145/36562982:CoNEXT2(1-22)Online publication date: 13-Jun-2024
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Khani MSalavatipour M(2016)Improved approximations for buy-at-bulk and shallow-light $$k$$k-Steiner trees and $$(k,2)$$(k,2)-subgraphJournal of Combinatorial Optimization10.1007/s10878-014-9774-531:2(669-685)Online publication date: 1-Feb-2016
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Approximation Algorithms for Non-Uniform Buy-at-Bulk Network Design

Parallel probabilistic tree embeddings, k-median, and buy-at-bulk network design

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