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Lasserre Integrality Gaps for Graph Spanners and Related Problems

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Approximation and Online Algorithms (WAOA 2020)

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Abstract

There has been significant recent progress on algorithms for approximating graph spanners, i.e., algorithms which approximate the best spanner for a given input graph. Essentially all of these algorithms use the same basic LP relaxation, so a variety of papers have studied the limitations of this approach and proved integrality gaps for this LP. We extend these results by showing that even the strongest lift-and-project methods cannot help significantly, by proving polynomial integrality gaps even for \(n^{\varOmega (\varepsilon )}\) levels of the Lasserre hierarchy, for both the directed and undirected spanner problems. We also extend these integrality gaps to related problems, notably Directed Steiner Network and Shallow-Light Steiner Network.

Supported in part by NSF award CCF-1909111.

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Acknowledgements

The authors would like to thank Amitabh Basu for many helpful discussions.

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Correspondence to Michael Dinitz .

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Dinitz, M., Nazari, Y., Zhang, Z. (2021). Lasserre Integrality Gaps for Graph Spanners and Related Problems. In: Kaklamanis, C., Levin, A. (eds) Approximation and Online Algorithms. WAOA 2020. Lecture Notes in Computer Science(), vol 12806. Springer, Cham. https://doi.org/10.1007/978-3-030-80879-2_7

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  • DOI: https://doi.org/10.1007/978-3-030-80879-2_7

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