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On the Communication Complexity of Maximum Matching and Negative-Weight Shortest Paths

Authors Yu Cheng , Tianle Jiang , Pachara Sawettamalya , Huacheng Yu

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LIPIcs.ESA.2026.72.pdf
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Subject Classification

ACM Subject Classification
  • Theory of computation → Graph algorithms analysis
  • Theory of computation → Communication complexity
Keywords
  • Graph algorithms
  • communication complexity
  • maximum matching
  • negative-weight shortest paths

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Abstract

We revisit several fundamental graph problems in the deterministic two-party communication model. Our main contributions include:  
- We give a new Õ(n^{3/2})-bit protocol for computing a maximum matching in general graphs. While the same upper bound can be obtained by simulating the classic algorithms of Micali-Vazirani [Silvio Micali and Vijay V. Vazirani, 1980] and Gabow [Harold N. Gabow, 2017], our protocol is conceptually simple and avoids the intricacies of finding a maximal set of shortest augmenting paths. 
- We give a new Õ(n)-bit protocol for negative-cycle detection and negative-weight single-source shortest paths. Our protocol simplifies that of Blikstad et al. [Joakim Blikstad et al., 2022] by replacing a long chain of reductions with a more direct approach based on vertex potentials. 
- We give a combinatorial Õ(n)-bit protocol for computing a maximum matching in bipartite graphs, obtained by reinterpreting the near-linear communication protocol of Blikstad et al. [Joakim Blikstad et al., 2022] through a discretized analysis.  Together, these results provide simpler protocols for several basic graph problems. We hope they will inspire further advances on the communication complexity of a wide range of graph problems.

Cite As Get BibTex

Yu Cheng, Tianle Jiang, Pachara Sawettamalya, and Huacheng Yu. On the Communication Complexity of Maximum Matching and Negative-Weight Shortest Paths. In 34th Annual European Symposium on Algorithms (ESA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 388, pp. 72:1-72:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.ESA.2026.72

Author Details

Yu Cheng
  • Department of Computer Science, Brown University, Providence, RI, USA
Tianle Jiang
  • Department of Computer Science, Duke University, Durham, NC, USA
Pachara Sawettamalya
  • Department of Computer Science, Princeton University, Princeton, NJ, USA
Huacheng Yu
  • Department of Computer Science, Princeton University, Princeton, NJ, USA

Funding

  • Cheng, Yu: Supported in part by NSF Award CCF-2307106.
  • Jiang, Tianle: Supported in part by NSF Award IIS-2402823. Part of the work was done while visiting Brown University.
  • Sawettamalya, Pachara: Supported in part by NSF CAREER Award CCF-2339942.
  • Yu, Huacheng: Supported in part by NSF CAREER Award CCF-2339942.

References

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