Adaptive-Adversary-Robust Algorithms via Small Copy Tree Embeddings

Authors Bernhard Haepler, D. Ellis Hershkowitz, Goran Zuzic



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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

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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

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.

Subject Classification

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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