Massively Parallel Computation in a Heterogeneous Regime

Orr Fischer, Adi Horowitz, Rotem Oshman

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


Massively-parallel graph algorithms have received extensive attention over the past decade, with research focusing on three memory regimes: the superlinear regime, the near-linear regime, and the sublinear regime. The sublinear regime is the most desirable in practice, but conditional hardness results point towards its limitations. In this work we study a heterogeneous model, where the memory of the machines varies in size. We focus mostly on the heterogeneous setting created by adding a single near-linear machine to the sublinear MPC regime, and show that even a single large machine suffices to circumvent most of the conditional hardness results for the sublinear regime: for graphs with n vertices and m edges, we give (a) an MST algorithm that runs in O(łogłog(m/n)) rounds; (b) an algorithm that constructs an O(k)-spanner of size O(n^1+1/k ) in O(1) rounds; and (c) a maximal-matching algorithm that runs in O(g łog(m/n) łogłog(m/n)) rounds. We also observe that the best known near-linear MPC algorithms for several other graph problems which are conjectured to be hard in the sublinear regime (minimum cut, maximal independent set, and vertex coloring) can easily be transformed to work in the heterogeneous MPC model with a single near-linear machine, while retaining their original round complexity in the near-linear regime. If the large machine is allowed to have superlinear memory, all of the problems above can be solved in O(1) rounds.

Original languageEnglish
Title of host publicationPODC 2022 - Proceedings of the 2022 ACM Symposium on Principles of Distributed Computing
PublisherAssociation for Computing Machinery
Number of pages11
ISBN (Electronic)9781450392624
StatePublished - 20 Jul 2022
Event41st ACM Symposium on Principles of Distributed Computing, PODC 2022 - Salerno, Italy
Duration: 25 Jul 202229 Jul 2022

Publication series

NameProceedings of the Annual ACM Symposium on Principles of Distributed Computing


Conference41st ACM Symposium on Principles of Distributed Computing, PODC 2022


  • heterogeneous memory regime
  • massively parallel computation


Dive into the research topics of 'Massively Parallel Computation in a Heterogeneous Regime'. Together they form a unique fingerprint.

Cite this