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Massively Parallel Approximate Distance Sketches

Authors Michael Dinitz, Yasamin Nazari

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Author Details

Michael Dinitz
  • Johns Hopkins University, Baltimore, MD, United States
Yasamin Nazari
  • Johns Hopkins University, Baltimore, MD, United States

Funding

This work supported is in part by NSF awards CCF-1464239 and CCF-1909111.

Acknowledgements

The authors are thankful to Goran Zuzic for helpful discussions.

Cite As Get BibTex

Michael Dinitz and Yasamin Nazari. Massively Parallel Approximate Distance Sketches. In 23rd International Conference on Principles of Distributed Systems (OPODIS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 153, pp. 35:1-35:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020) https://doi.org/10.4230/LIPIcs.OPODIS.2019.35

Abstract

Data structures that allow efficient distance estimation (distance oracles, distance sketches, etc.) have been extensively studied, and are particularly well studied in centralized models and classical distributed models such as CONGEST. We initiate their study in newer (and arguably more realistic) models of distributed computation: the Congested Clique model and the Massively Parallel Computation (MPC) model. We provide efficient constructions in both of these models, but our core results are for MPC. In MPC we give two main results: an algorithm that constructs stretch/space optimal distance sketches but takes a (small) polynomial number of rounds, and an algorithm that constructs distance sketches with worse stretch but that only takes polylogarithmic rounds. 
Along the way, we show that other useful combinatorial structures can also be computed in MPC. In particular, one key component we use to construct distance sketches are an MPC construction of the hopsets of [Elkin and Neiman, 2016]. This result has additional applications such as the first polylogarithmic time algorithm for constant approximate single-source shortest paths for weighted graphs in the low memory MPC setting.

Subject Classification

ACM Subject Classification
  • Theory of computation → Massively parallel algorithms
Keywords
  • Distance Sketches
  • Massively Parallel Computation
  • Distance Oracles
  • Single-Source Shortest Paths

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