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Real-Weighted Diameter and Eccentricities of Minor-Free and Bounded VC-Dimension Graphs in Truly Subquadratic Time

Author Da Wei Zheng

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LIPIcs.ESA.2026.61.pdf
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Subject Classification

ACM Subject Classification
  • Theory of computation → Shortest paths
Keywords
  • Diameter
  • eccentricities
  • minor-free graphs
  • real weights
  • VC-dimension

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Abstract

We present the first truly subquadratic time algorithm to compute diameter and eccentricities in real-weighted directed graphs with constant distance VC-dimension and strongly sublinear-sized balanced separators. For real-weighted K_h-minor-free digraphs, this runs in O(n^{2-1/(2h-2)} polylog(n)) time.
Prior to this work, truly subquadratic time computation of diameter was only known for real-weighted planar graphs, while extensions to broader classes like minor-free graphs were restricted to unweighted settings. In particular, existing algorithms that use VC-dimension [Ducoffe, Habib, Viennot; SICOMP 2022] [Le, Wulff-Nilsen; SODA 2024] [Chan, Chang, Gao, Le, Kisfaludi-Bak, Zheng; FOCS 2025] work with small integer weights, but do not naturally generalize to real weights. We overcome this barrier by introducing a randomized search-to-decision reduction, demonstrating that VC-dimension is a sufficiently powerful tool in the real-weighted regime.

Cite As Get BibTex

Da Wei Zheng. Real-Weighted Diameter and Eccentricities of Minor-Free and Bounded VC-Dimension Graphs in Truly Subquadratic Time. In 34th Annual European Symposium on Algorithms (ESA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 388, pp. 61:1-61:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.ESA.2026.61

Author Details

Da Wei Zheng
  • Institute of Science and Technology Austria, Klosterneuburg, Austria

Funding

  • Zheng, Da Wei: This project has received funding from the Austrian Science Fund (FWF) grant https://www.doi.org/10.55776/I5982. For open access purposes, the author has applied a CC BY public copyright license to any author-accepted manuscript version arising from this submission.

Acknowledgements

Thanks to Jie Gao for feedback on a preliminary version of the manuscript.

References

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