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Faster Diameter Computation in Graphs of Bounded Euler Genus

Authors Kacper Kluk , Marcin Pilipczuk , Michał Pilipczuk , Giannos Stamoulis

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ACM Subject Classification
  • Mathematics of computing → Graph algorithms
  • Mathematics of computing → Graphs and surfaces
  • Mathematics of computing → Paths and connectivity problems
  • Theory of computation → Fixed parameter tractability
  • Theory of computation → Shortest paths
Keywords
  • Diameter
  • eccentricity
  • subquadratic algorithms
  • surface-embeddable graphs

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Abstract

We show that for any fixed integer k ⩾ 0, there exists an algorithm that computes the diameter and the eccentricies of all vertices of an input unweighted, undirected n-vertex graph of Euler genus at most k in time 𝒪_k(n^{2-1/25}). Furthermore, for the more general class of graphs that can be constructed by clique-sums from graphs that are of Euler genus at most k after deletion of at most k vertices, we show an algorithm for the same task that achieves the running time bound 𝒪_k(n^{2-1/356} log^{6k} n). Up to today, the only known subquadratic algorithms for computing the diameter in those graph classes are that of [Ducoffe, Habib, Viennot; SICOMP 2022], [Le, Wulff-Nilsen; SODA 2024], and [Duraj, Konieczny, Potępa; ESA 2024]. These algorithms work in the more general setting of K_h-minor-free graphs, but the running time bound is 𝒪_h(n^{2-c_h}) for some constant c_h > 0 depending on h. That is, our savings in the exponent of the polynomial function of n, as compared to the naive quadratic algorithm, are independent of the parameter k.
The main technical ingredient of our work is an improved bound on the number of distance profiles, as defined in [Le, Wulff-Nilsen; SODA 2024], in graphs of bounded Euler genus.

Cite As Get BibTex

Kacper Kluk, Marcin Pilipczuk, Michał Pilipczuk, and Giannos Stamoulis. Faster Diameter Computation in Graphs of Bounded Euler Genus. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 109:1-109:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ICALP.2025.109

Author Details

Kacper Kluk
  • Institute of Informatics, University of Warsaw, Poland
Marcin Pilipczuk
  • Institute of Informatics, University of Warsaw, Poland
Michał Pilipczuk
  • Institute of Informatics, University of Warsaw, Poland
Giannos Stamoulis
  • Université Paris Cité, CNRS, IRIF, F-75013, Paris, France

Funding

K.K. and Ma.P. are supported by Polish National Science Centre SONATA BIS-12 grant number 2022/46/E/ST6/00143. This work is a part of project BOBR (Mi.P., G.S.) that has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 948057). In particular, a majority of work on this manuscript was done while G.S. was affiliated with University of Warsaw.

Acknowledgements

Marcin thanks Jacob Holm, Eva Rotenberg, and Erik Jan van Leeuwen for many discussions on subquadratic algorithms for diameter while his stay on sabbatical in Copenhagen.

References

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