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The Complexity Landscape of Dynamic Distributed Subgraph Finding

Authors Yi-Jun Chang , Lyuting Chen , Yanyu Chen , Gopinath Mishra , Mingyang Yang

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  • Theory of computation → Distributed algorithms
Keywords
  • Distributed algorithms
  • dynamic algorithms
  • subgraph finding

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Abstract

Bonne and Censor-Hillel (ICALP 2019) initiated the study of distributed subgraph finding in dynamic networks of limited bandwidth. For the case where the target subgraph is a clique, they determined the tight bandwidth complexity bounds in nearly all settings. However, several open questions remain, and very little is known about finding subgraphs beyond cliques. In this work, we consider these questions and explore subgraphs beyond cliques in the deterministic setting.
For finding cliques, we establish an Ω(log log n) bandwidth lower bound for one-round membership-detection under edge insertions only and an Ω(log log log n) bandwidth lower bound for one-round detection under both edge insertions and node insertions. Moreover, we demonstrate new algorithms to show that our lower bounds are tight in bounded-degree networks when the target subgraph is a triangle. Prior to our work, no lower bounds were known for these problems.
For finding subgraphs beyond cliques, we present a complete characterization of the bandwidth complexity of the membership-listing problem for every target subgraph, every number of rounds, and every type of topological change: node insertions, node deletions, edge insertions, and edge deletions. We also show partial characterizations for one-round membership-detection and listing.

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Yi-Jun Chang, Lyuting Chen, Yanyu Chen, Gopinath Mishra, and Mingyang Yang. The Complexity Landscape of Dynamic Distributed Subgraph Finding. In 39th International Symposium on Distributed Computing (DISC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 356, pp. 22:1-22:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.DISC.2025.22

Author Details

Yi-Jun Chang
  • National University of Singapore, Singapore
Lyuting Chen
  • National University of Singapore, Singapore
Yanyu Chen
  • National University of Singapore, Singapore
Gopinath Mishra
  • National University of Singapore, Singapore
Mingyang Yang
  • National University of Singapore, Singapore

Funding

The research is supported by the Ministry of Education, Singapore, under its Academic Research Fund Tier 1 (24-1323-A0001). Any opinions, findings and conclusions or recommendations expressed in this material are those of the authors and do not reflect the views of the Ministry of Education, Singapore.

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