Hardness of distributed optimization

Nir Bacrach, Keren Censor-Hillel, Michal Dory, Yuval Efron, Dean Leitersdorf, Ami Paz

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


This paper studies lower bounds for fundamental optimization problems in the CONGEST model. We show that solving problems exactly in this model can be a hard task, by providing tildemega (n2) lower bounds for cornerstone problems, such as minimum dominating set (MDS), Hamiltonian path, Steiner tree and max-cut. These are almost tight, since all of these problems can be solved optimally in O(n2) rounds. Moreover, we show that even in bounded-degree graphs and even in simple graphs with maximum degree 5 and logarithmic diameter, it holds that various tasks, such as finding a maximum independent set (MaxIS) or a minimum vertex cover, are still difficult, requiring a near-tight number of tilde (n) rounds. Furthermore, we show that in some cases even approximations are difficult, by providing an tilde (n2) lower bound for a (7/8+)-approximation for MaxIS, and a nearly-linear lower bound for an O(log n )-approximation for the k-MDS problem for any constant k geq 2, as well as for several variants of the Steiner tree problem. Our lower bounds are based on a rich variety of constructions that leverage novel observations, and reductions among problems that are specialized for the CONGEST model. However, for several additional approximation problems, as well as for exact computation of some central problems in P, such as maximum matching and max flow, we show that such constructions cannot be designed, by which we exemplify some limitations of this framework.

Original languageEnglish
Title of host publicationPODC 2019 - Proceedings of the 2019 ACM Symposium on Principles of Distributed Computing
PublisherAssociation for Computing Machinery
Number of pages10
ISBN (Electronic)9781450362177
StatePublished - 16 Jul 2019
Externally publishedYes
Event38th ACM Symposium on Principles of Distributed Computing, PODC 2019 - Toronto, Canada
Duration: 29 Jul 20192 Aug 2019

Publication series

NameProceedings of the Annual ACM Symposium on Principles of Distributed Computing


Conference38th ACM Symposium on Principles of Distributed Computing, PODC 2019

Bibliographical note

Publisher Copyright:
© 2019 ACM.


  • Approximation algorithms
  • Communication complexity
  • Congest
  • Distributed computing
  • Optimization problems

ASJC Scopus subject areas

  • Software
  • Hardware and Architecture
  • Computer Networks and Communications


Dive into the research topics of 'Hardness of distributed optimization'. Together they form a unique fingerprint.

Cite this