Approximating directed buy-at-bulk network design
WAOA'10 Proceedings of the 8th international conference on Approximation and online algorithms
Buy-at-Bulk Network Design with Protection
Mathematics of Operations Research
A new approximation algorithm for the selective single-sink buy-at-bulk problem in network design
COCOA'11 Proceedings of the 5th international conference on Combinatorial optimization and applications
Improved approximation algorithms for Directed Steiner Forest
Journal of Computer and System Sciences
Improved approximations for buy-at-bulk and shallow-light k-steiner trees and (k,2)-subgraph
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
A new approximation algorithm for the Selective Single-Sink Buy-at-Bulk problem in network design
Journal of Combinatorial Optimization
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Buy-at-bulk network design problems arise in settings where the costs for purchasing or installing equipment exhibit economies of scale. The objective is to build a network of cheapest cost to support a given multicommodity flow demand between node pairs. We present approximation algorithms for buy-at-bulk network design problems with costs on both edges and nodes of an undirected graph. Our main result is the first poly-logarithmic approximation ratio for the non-uniform problem that allows different cost functions on each edge and node; the ratio we achieve is $O(\log^4 h)$, where $h$ is the number of demand pairs. In addition we present an $O(\log h)$ approximation for the single sink problem. Poly-logarithmic ratios for some related problems are also obtained. Our algorithm for the multicommodity problem is obtained via a reduction to the single source problem using the notion of junction trees. We believe that this presents a simple yet useful general technique for network design problems.