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A unified algorithm for degree bounded survivable network design

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Abstract

We present an approximation algorithm for the minimum bounded degree Steiner network problem that returns a Steiner network of cost at most two times the optimal and the degree on each vertex \(v\) is at most \(\min \{b_v + 3r_{\mathrm{max}}, 2b_v+2\}\), where \(r_{\mathrm{max}}\) is the maximum connectivity requirement and \(b_v\) is the given degree bound on \(v\). This unifies, simplifies, and improves the previous results for this problem.

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Notes

  1. For instance, it was not known how to combine the results in [14, 15] to obtain a \((2, \min \{b_v+6r_{\mathrm{max}}+3, 2b_v+2\})\)-approximation algorithm for the problem.

  2. In particular, the analysis of the \((2,b_v+3)\) result is significantly simpler than that in [14].

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Acknowledgments

We thank the anonymous reviewers for comments that improve the presentation of the paper. This research is partially supported by HK RGC Grant 2150701.

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  1. Department of Computer Science and Engineering, The Chinese University of Hong Kong, Shatin, Hong Kong

    Lap Chi Lau & Hong Zhou

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  1. Lap Chi Lau
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  2. Hong Zhou
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Correspondence to Hong Zhou.

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Lau, L.C., Zhou, H. A unified algorithm for degree bounded survivable network design. Math. Program. 154, 515–532 (2015). https://doi.org/10.1007/s10107-015-0858-5

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  • DOI: https://doi.org/10.1007/s10107-015-0858-5

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