Brief Announcement: Massively Parallel Approximate Distance Sketches

Authors Michael Dinitz, Yasamin Nazari

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

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Michael Dinitz and Yasamin Nazari. Brief Announcement: Massively Parallel Approximate Distance Sketches. In 33rd International Symposium on Distributed Computing (DISC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 146, pp. 42:1-42:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


Data structures that allow efficient distance estimation have been extensively studied both in centralized models and classical distributed models. 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. 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 is 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
  • Distance Sketches
  • Massively Parallel Computation
  • Congested Clique


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