Dynamic Constant Time Parallel Graph Algorithms with Sub-Linear Work

Authors Jonas Schmidt, Thomas Schwentick

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Jonas Schmidt
  • TU Dortmund University, Germany
Thomas Schwentick
  • TU Dortmund University, Germany


We are grateful to Jens Keppeler and Christopher Spinrath for careful proof reading.

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Jonas Schmidt and Thomas Schwentick. Dynamic Constant Time Parallel Graph Algorithms with Sub-Linear Work. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 80:1-80:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


The paper proposes dynamic parallel algorithms for connectivity and bipartiteness of undirected graphs that require constant time and 𝒪(n^{1/2+ε}) work on the CRCW PRAM model. The work of these algorithms almost matches the work of the 𝒪(log n) time algorithm for connectivity by Kopelowitz et al. (2018) on the EREW PRAM model and the time of the sequential algorithm for bipartiteness by Eppstein et al. (1997). In particular, we show that the sparsification technique, which has been used in both mentioned papers, can in principle also be used for constant time algorithms in the CRCW PRAM model, despite the logarithmic depth of sparsification trees.

Subject Classification

ACM Subject Classification
  • Theory of computation → Dynamic graph algorithms
  • Theory of computation → Parallel algorithms
  • Dynamic parallel algorithms
  • Undirected connectivity
  • Bipartiteness


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