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A new approximation algorithm for the Selective Single-Sink Buy-at-Bulk problem in network design

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Abstract

The Selective Single-Sink Buy-at-Bulk problem was proposed by Awerbuch and Azar (FOCS 1997). For a long time, the only known non-trivial approach to approximate this problem is the tree-embedding method initiated by Bartal (FOCS 1996). In this paper, we give a thoroughly different approximation approach for the problem with approximation ratio \(O(\sqrt{q})\), where q is the number of source terminals in the problem instance. Our approach is based on a mixed strategy of LP-rounding and the greedy method. When the number q (which is always at most n) is relatively small (say, q=o(log2 n)), our approximation ratio \(O(\sqrt{q})\) is better than the currently known best ratio O(logn), where n is the number of vertices in the input graph.

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Acknowledgements

The author would like to thank the anonymous reviewers for their helpful comments which improve the representation of the paper. And, the author is grateful to an anonymous reviewer for his/her suggestion significantly simplifies the construction of the instance in Sect. 5.

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Authors and Affiliations

  1. School of Computer Science and Technology, Shandong University, Jinan, 250101, China

    Peng Zhang

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  1. Peng Zhang
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Correspondence to Peng Zhang.

Additional information

A preliminary version of this paper appeared in the Proceedings of the 5th Annual International Conference on Combinatorial Optimization and Applications (COCOA), pp. 525–536 (Zhang 2011).

This work is supported by the National Natural Science Foundation of China (60970003), China Postdoctoral Science Foundation (200902562), the Special Foundation of Shandong Province Postdoctoral Innovation Project (200901010), and the Independent Innovation Foundation of Shandong University (2012TS072).

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Zhang, P. A new approximation algorithm for the Selective Single-Sink Buy-at-Bulk problem in network design. J Comb Optim 27, 663–678 (2014). https://doi.org/10.1007/s10878-012-9544-1

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