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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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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.

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

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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References

  1. Ajit Agrawal, Philip Klein, and Ramamoorthi Ravi. When trees collide: An approximation algorithm for the generalized steiner problem on networks. SIAM Journal on Computing, 24(3):440-456, 1995. Google Scholar
  2. Noga Alon, Baruch Awerbuch, Yossi Azar, Niv Buchbinder, and Joseph Naor. A general approach to online network optimization problems. ACM Transactions on Algorithms (TALG), 2(4):640-660, 2006. Google Scholar
  3. Noga Alon, Richard M Karp, David Peleg, and Douglas West. A graph-theoretic game and its application to the k-server problem. SIAM Journal on Computing, 24(1):78-100, 1995. Google Scholar
  4. Baruch Awerbuch and Yossi Azar. Buy-at-bulk network design. In Symposium on Foundations of Computer Science (FOCS), pages 542-547. IEEE, 1997. Google Scholar
  5. Nikhil Bansal, Niv Buchbinder, Aleksander Madry, and Joseph Naor. A polylogarithmic-competitive algorithm for the k-server problem. In Symposium on Foundations of Computer Science (FOCS), pages 267-276. IEEE, 2011. Google Scholar
  6. Yair Bartal. Probabilistic approximation of metric spaces and its algorithmic applications. In Symposium on Foundations of Computer Science (FOCS), pages 184-193. IEEE, 1996. Google Scholar
  7. Yair Bartal. Graph decomposition lemmas and their role in metric embedding methods. In Annual European Symposium on Algorithms (ESA), pages 89-97. Springer, 2004. Google Scholar
  8. Yair Bartal, Avrim Blum, Carl Burch, and Andrew Tomkins. A polylog (n)-competitive algorithm for metrical task systems. In Annual ACM Symposium on Theory of Computing (STOC), pages 711-719, 1997. Google Scholar
  9. Yair Bartal and Manor Mendel. Multi-embedding and path approximation of metric spaces. In Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), volume 3, pages 424-433, 2003. Google Scholar
  10. Marcin Bienkowski, Bjorn Feldkord, and Pawel Schmidt. A nearly optimal deterministic online algorithm for non-metric facility location. arXiv preprint, 2020. URL: http://arxiv.org/abs/2007.07025.
  11. Niv Buchbinder and Joseph Naor. The design of competitive online algorithms via a primal-dual approach. Now Publishers Inc, 2009. Google Scholar
  12. Moses Charikar, Chandra Chekuri, Ashish Goel, Sudipto Guha, and Serge Plotkin. Approximating a finite metric by a small number of tree metrics. In Symposium on Foundations of Computer Science (FOCS), pages 379-388. IEEE, 1998. Google Scholar
  13. Kedar Dhamdhere, Vineet Goyal, R Ravi, and Mohit Singh. How to pay, come what may: Approximation algorithms for demand-robust covering problems. In Symposium on Foundations of Computer Science (FOCS), pages 367-376. IEEE, 2005. Google Scholar
  14. Matthias Englert and Harald Räcke. Reordering buffers with logarithmic diameter dependency for trees. In Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 1224-1234. SIAM, 2017. Google Scholar
  15. Matthias Englert, Harald Räcke, and Matthias Westermann. Reordering buffers for general metric spaces. In Annual ACM Symposium on Theory of Computing (STOC), 2007. Google Scholar
  16. Guy Even, Guy Kortsarz, and Wolfgang Slany. On network design problems: fixed cost flows and the covering steiner problem. ACM Transactions on Algorithms (TALG), 1(1):74-101, 2005. Google Scholar
  17. Jittat Fakcharoenphol, Satish Rao, and Kunal Talwar. A tight bound on approximating arbitrary metrics by tree metrics. Journal of Computer and System Sciences, 69(3):485-497, 2004. Google Scholar
  18. Uriel Feige, Kamal Jain, Mohammad Mahdian, and Vahab Mirrokni. Robust combinatorial optimization with exponential scenarios. In Conference on Integer Programming and Combinatorial Optimization (IPCO), pages 439-453. Springer, 2007. Google Scholar
  19. Amos Fiat and Manor Mendel. Better algorithms for unfair metrical task systems and applications. SIAM Journal on Computing, 32(6):1403-1422, 2003. Google Scholar
  20. Arnold Filtser. Clan embeddings into trees, and low treewidth graphs. arXiv preprint, 2021. URL: http://arxiv.org/abs/2101.01146.
  21. Naveen Garg, Goran Konjevod, and R Ravi. A polylogarithmic approximation algorithm for the group steiner tree problem. Journal of Algorithms, 37(1):66-84, 2000. Google Scholar
  22. Daniel Golovin, Vineet Goyal, and R Ravi. Pay today for a rainy day: improved approximation algorithms for demand-robust min-cut and shortest path problems. In International Symposium on Theoretical Aspects of Computer Science (STACS), pages 206-217. Springer, 2006. Google Scholar
  23. Xiangyu Guo, Janardhan Kulkarni, Shi Li, and Jiayi Xian. On the facility location problem in online and dynamic models. In International Workshop on Approximation Algorithms for Combinatorial Optimization Problems (APPROX). Schloss Dagstuhl-Leibniz-Zentrum für Informatik, 2020. Google Scholar
  24. Anupam Gupta, Mohammad T Hajiaghayi, and Harald Räcke. Oblivious network design. In Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 970-979, 2006. Google Scholar
  25. Anupam Gupta, Viswanath Nagarajan, and R Ravi. Robust and maxmin optimization under matroid and knapsack uncertainty sets. ACM Transactions on Algorithms (TALG), 12(1):1-21, 2015. Google Scholar
  26. Anupam Gupta, Viswanath Nagarajan, and Ramamoorthi Ravi. Thresholded covering algorithms for robust and max-min optimization. In International Colloquium on Automata, Languages and Programming (ICALP), pages 262-274. Springer, 2010. Google Scholar
  27. Anupam Gupta and Aravind Srinivasan. An improved approximation ratio for the covering steiner problem. Theory of Computing, 2(1):53-64, 2006. Google Scholar
  28. Varun Gupta, Ravishankar Krishnaswamy, and Sai Sandeep. Permutation strikes back: The power of recourse in online metric matching. In International Workshop on Approximation Algorithms for Combinatorial Optimization Problems (APPROX), 2020. Google Scholar
  29. Bernhard Haeupler, D Ellis Hershkowitz, and Goran Zuzic. Tree embeddings for hop-constrained network design. Annual ACM Symposium on Theory of Computing (STOC), 2021. Google Scholar
  30. D Ellis Hershkowitz, R Ravi, and Sahil Singla. Prepare for the expected worst: Algorithms for reconfigurable resources under uncertainty. In International Workshop on Approximation Algorithms for Combinatorial Optimization Problems (APPROX), 2019. Google Scholar
  31. Makoto Imase and Bernard M Waxman. Dynamic steiner tree problem. SIAM Journal on Discrete Mathematics, 4(3):369-384, 1991. Google Scholar
  32. Richard M Karp. A 2k-competitive algorithm for the circle. Manuscript, August, 5, 1989. Google Scholar
  33. Adam Kasperski and Paweł Zieliński. On the approximability of robust spanning tree problems. Theoretical Computer Science, 412(4-5):365-374, 2011. Google Scholar
  34. Rohit Khandekar, Guy Kortsarz, Vahab Mirrokni, and Mohammad R Salavatipour. Two-stage robust network design with exponential scenarios. In Annual European Symposium on Algorithms (ESA), pages 589-600. Springer, 2008. Google Scholar
  35. Goran Konjevod, Ramamoorthi Ravi, and Aravind Srinivasan. Approximation algorithms for the covering steiner problem. Random Structures & Algorithms, 20(3):465-482, 2002. Google Scholar
  36. Joseph Naor, Debmalya Panigrahi, and Mohit Singh. Online node-weighted steiner tree and related problems. In Symposium on Foundations of Computer Science (FOCS), pages 210-219. IEEE, 2011. Google Scholar
  37. Harald Racke. Minimizing congestion in general networks. In Symposium on Foundations of Computer Science (FOCS), pages 43-52. IEEE, 2002. Google Scholar
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