Lasserre Integrality Gaps for Graph Spanners and Related Problems

Michael Dinitz; Yasamin Nazari; Zeyu Zhang

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arXiv · 1905.07468

Lasserre Integrality Gaps for Graph Spanners and Related Problems

Michael Dinitz·Yasamin Nazari·Zeyu Zhang

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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 in a variety of settings. We extend these results by showing that even the strongest lift-and-project methods cannot help significantly, by proving polynomial integrality gaps even for $n^{\Omega(\epsilon)}$ 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.

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BibTeX RIS

Michael Dinitz, Yasamin Nazari, Zeyu Zhang. 2019-05-17. Lasserre Integrality Gaps for Graph Spanners and Related Problems. https://arxiv.org/abs/1905.07468

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