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Adaptive-Adversary-Robust Algorithms via Small Copy Tree Embeddings

Authors: Bernhard Haepler, D. Ellis Hershkowitz, and Goran Zuzic

Published in: LIPIcs, Volume 244, 30th Annual European Symposium on Algorithms (ESA 2022)

Embeddings of graphs into distributions of trees that preserve distances in expectation are a cornerstone of many optimization algorithms. Unfortunately, online or dynamic algorithms which use these embeddings seem inherently randomized and ill-suited against adaptive adversaries. In this paper we provide a new tree embedding which addresses these issues by deterministically embedding a graph into a single tree containing O(log n) copies of each vertex while preserving the connectivity structure of every subgraph and O(log² n)-approximating the cost of every subgraph. Using this embedding we obtain the first deterministic bicriteria approximation algorithm for the online covering Steiner problem as well as the first poly-log approximations for demand-robust Steiner forest, group Steiner tree and group Steiner forest.

Cite as

Bernhard Haepler, D. Ellis Hershkowitz, and Goran Zuzic. Adaptive-Adversary-Robust Algorithms via Small Copy Tree Embeddings. In 30th Annual European Symposium on Algorithms (ESA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 244, pp. 63:1-63:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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  author =	{Haepler, Bernhard and Hershkowitz, D. Ellis and Zuzic, Goran},
  title =	{{Adaptive-Adversary-Robust Algorithms via Small Copy Tree Embeddings}},
  booktitle =	{30th Annual European Symposium on Algorithms (ESA 2022)},
  pages =	{63:1--63:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-247-1},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{244},
  editor =	{Chechik, Shiri and Navarro, Gonzalo and Rotenberg, Eva and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2022.63},
  URN =		{urn:nbn:de:0030-drops-170016},
  doi =		{10.4230/LIPIcs.ESA.2022.63},
  annote =	{Keywords: Tree metrics, metric embeddings, approximation algorithms, group Steiner forest, group Steiner tree, demand-robust algorithms, online algorithms, deterministic algorithms}
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