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Adaptive-Adversary-Robust Algorithms via Small Copy Tree Embeddings

Authors Bernhard Haepler, D. Ellis Hershkowitz, Goran Zuzic

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  • 14 pages

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ACM Subject Classification
  • Mathematics of computing → Trees
  • Mathematics of computing → Approximation algorithms
  • Mathematics of computing → Paths and connectivity problems
  • Theory of computation → Random projections and metric embeddings
Keywords
  • Tree metrics
  • metric embeddings
  • approximation algorithms
  • group Steiner forest
  • group Steiner tree
  • demand-robust algorithms
  • online algorithms
  • deterministic algorithms

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Abstract

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 Get BibTex

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) https://doi.org/10.4230/LIPIcs.ESA.2022.63

Author Details

Bernhard Haepler
  • Carnegie Mellon University, Pittsburgh, PA, USA
  • ETH Zürich, Switzerland
D. Ellis Hershkowitz
  • Carnegie Mellon University, Pittsburgh, PA, USA
Goran Zuzic
  • ETH Zürich, Switzerland

Funding

Supported in part by NSF grants CCF-1527110, CCF-1618280, CCF-1814603, CCF-1910588, NSF CAREER award CCF-1750808, a Sloan Research Fellowship, funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (ERC grant agreement 949272) and Swiss National Foundation (project grant 200021-184735).
  • Hershkowitz, D. Ellis: Supported by the Air Force Office of Scientific Research under award number FA9550-20-1-0080.

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