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Distance Computations in the Hybrid Network Model via Oracle Simulations

Authors Keren Censor-Hillel , Dean Leitersdorf, Volodymyr Polosukhin



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Author Details

Keren Censor-Hillel
  • Technion - Israel Institute of Technology, Haifa, Israel
Dean Leitersdorf
  • Technion - Israel Institute of Technology, Haifa, Israel
Volodymyr Polosukhin
  • Technion - Israel Institute of Technology, Haifa, Israel

Acknowledgements

The authors would like to thank Michal Dory and Yuval Efron for various helpful conversations. We also thank Fabian Kuhn for sharing a preprint of [Kuhn and Schneider, 2020] with us.

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Keren Censor-Hillel, Dean Leitersdorf, and Volodymyr Polosukhin. Distance Computations in the Hybrid Network Model via Oracle Simulations. In 38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 187, pp. 21:1-21:19, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)
https://doi.org/10.4230/LIPIcs.STACS.2021.21

Abstract

The Hybrid network model was introduced in [Augustine et al., SODA '20] for laying down a theoretical foundation for networks which combine two possible modes of communication: One mode allows high-bandwidth communication with neighboring nodes, and the other allows low-bandwidth communication over few long-range connections at a time. This fundamentally abstracts networks such as hybrid data centers, and class-based software-defined networks. Our technical contribution is a density-aware approach that allows us to simulate a set of oracles for an overlay skeleton graph over a Hybrid network. As applications of our oracle simulations, with additional machinery that we provide, we derive fast algorithms for fundamental distance-related tasks. One of our core contributions is an algorithm in the Hybrid model for computing exact weighted shortest paths from Õ(n^{1/3}) sources which completes in Õ(n^{1/3}) rounds w.h.p. This improves, in both the runtime and the number of sources, upon the algorithm of [Kuhn and Schneider, PODC ’20], which computes shortest paths from a single source in Õ(n^{2/5}) rounds w.h.p. We additionally show a 2-approximation for weighted diameter and a (1+ε)-approximation for unweighted diameter, both in Õ(n^{1/3}) rounds w.h.p., which is comparable to the ̃ Ω(n^{1/3}) lower bound of [Kuhn and Schneider, PODC ’20] for a (2-ε)-approximation for weighted diameter and an exact unweighted diameter. We also provide fast distance approximations from multiple sources and fast approximations for eccentricities.

Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed algorithms
Keywords
  • Distributed graph algorithms
  • Hybrid network model
  • Distance computations

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