Conditional Hardness Results for Massively Parallel Computation from Distributed Lower Bounds

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


Research units

  • Swiss Federal Institute of Technology Zurich
  • University of Freiburg


We present the first conditional hardness results for massively parallel algorithms for some central graph problems including (approximating) maximum matching, vertex cover, maximal independent set, and coloring. In some cases, these hardness results match or get close to the state of the art algorithms. Our hardness results are conditioned on a widely believed conjecture in massively parallel computation about the complexity of the connectivity problem. We also note that it is known that an unconditional variant of such hardness results might be somewhat out of reach for now, as it would lead to considerably improved circuit complexity lower bounds and would concretely imply that NC_1 is a proper subset of P. We obtain our conditional hardness result via a general method that lifts unconditional lower bounds from the well-studied LOCAL model of distributed computing to the massively parallel computation setting.


Original languageEnglish
Title of host publicationProceedings - 2019 IEEE 60th Annual Symposium on Foundations of Computer Science, FOCS 2019
Publication statusPublished - 6 Jan 2020
MoE publication typeA4 Article in a conference publication
EventAnnual Symposium on Foundations of Computer Science - Hotel Hyatt Regency Baltimore Inner Harbor, Baltimore, United States
Duration: 9 Nov 201912 Nov 2019


ConferenceAnnual Symposium on Foundations of Computer Science
Abbreviated titleFOCS
CountryUnited States
Internet address

ID: 38157421