Fast distributed algorithms for connectivity and MST in Large Graphs

Gopal Pandurangan, Peter Robinson, Michele Scquizzato

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


Motivated by the increasing need to understand the algorithmic foundations of distributed large-scale graph computations, we study a number of fundamental graph problems in amessage-passing model for distributed computing where k ≥ 2 machines jointly perform computations on graphs with n nodes (typically, n > k). The input graph is assumed to be initially randomly partitioned among the k machines, a common implementation in many real-world systems. Communication is point-To-point, and the goal is to minimize the number of communication rounds of the computation. Our main result is an (almost) optimal distributed randomized algorithm for graph connectivity. Our algorithm runs in Õ (n/k2) rounds ( Õ notation hides a polylog(n) factor and an additive polylog(n) term). This improves over the best previously known bound of Õ (n/k) [Klauck et al., SODA 2015] and is optimal (up to a polylogarithmic factor) in light of an existing lower bound of ω(n/k2). Our improved algorithm uses a bunch of techniques, including linear graph sketching, that prove useful in the design of efficient distributed graph algorithms. Using the connectivity algorithm as a building block, we then present fast randomized algorithms for computing minimum spanning trees, (approximate) min-cuts, and for many graph verification problems. All these algorithms take Õ (n/k2) rounds and are optimal up to polylogarithmic factors. We also show an almost matching lower bound of ω (n/k2) rounds for many graph verification problems by leveraging lower bounds in random-partition communication complexity.

Original languageEnglish (US)
Article numbera4
JournalACM Transactions on Parallel Computing
Issue number1
StatePublished - Sep 2018
Externally publishedYes


  • Distributed graph algorithms
  • Graph connectivity
  • Graph sketching
  • Minimum spanning trees

ASJC Scopus subject areas

  • Software
  • Modeling and Simulation
  • Hardware and Architecture
  • Computer Science Applications
  • Computational Theory and Mathematics


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