An Experimental Study of External Memory Algorithms for Connected Components

Authors Gerth Stølting Brodal, Rolf Fagerberg, David Hammer, Ulrich Meyer, Manuel Penschuck, Hung Tran

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Author Details

Gerth Stølting Brodal
  • Aarhus University, Denmark
Rolf Fagerberg
  • University of Southern Denmark, Odense, Denmark
David Hammer
  • Goethe Universität Frankfurt, Germany
  • University of Southern Denmark, Odense, Denmark
Ulrich Meyer
  • Goethe Universität Frankfurt, Germany
Manuel Penschuck
  • Goethe Universität Frankfurt, Germany
Hung Tran
  • Goethe Universität Frankfurt, Germany


Extensive calculations on the Goethe-HLR high-performance computer of the Goethe University Frankfurt were conducted for this research. The authors would like to acknowledge the CSC team for their support. We would also like to thank Peter Sanders for valuable feedback on an earlier draft of this paper.

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Gerth Stølting Brodal, Rolf Fagerberg, David Hammer, Ulrich Meyer, Manuel Penschuck, and Hung Tran. An Experimental Study of External Memory Algorithms for Connected Components. In 19th International Symposium on Experimental Algorithms (SEA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 190, pp. 23:1-23:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


We empirically investigate algorithms for solving Connected Components in the external memory model. In particular, we study whether the randomized O(Sort(E)) algorithm by Karger, Klein, and Tarjan can be implemented to compete with practically promising and simpler algorithms having only slightly worse theoretical cost, namely Borůvka’s algorithm and the algorithm by Sibeyn and collaborators. For all algorithms, we develop and test a number of tuning options. Our experiments are executed on a large set of different graph classes including random graphs, grids, geometric graphs, and hyperbolic graphs. Among our findings are: The Sibeyn algorithm is a very strong contender due to its simplicity and due to an added degree of freedom in its internal workings when used in the Connected Components setting. With the right tunings, the Karger-Klein-Tarjan algorithm can be implemented to be competitive in many cases. Higher graph density seems to benefit Karger-Klein-Tarjan relative to Sibeyn. Borůvka’s algorithm is not competitive with the two others.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Paths and connectivity problems
  • Theory of computation → Graph algorithms analysis
  • Connected Components
  • Experimental Evaluation
  • External Memory
  • Graph Algorithms
  • Randomization


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