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Optimal Adjacency Labels for Subgraphs of Cartesian Products

Authors Louis Esperet , Nathaniel Harms , Viktor Zamaraev

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Author Details

Louis Esperet
  • Laboratoire G-SCOP, Grenoble, France
Nathaniel Harms
  • EPFL, Lausanne, Switzerland
Viktor Zamaraev
  • University of Liverpool, UK

Funding

  • Esperet, Louis: Partially supported by the French ANR Projects GATO (ANR-16-CE40-0009-01), GrR (ANR-18-CE40-0032), TWIN-WIDTH (ANR-21-CE48-0014-01) and by LabEx PERSYVAL-lab (ANR-11-LABX-0025).
  • Harms, Nathaniel: This work was partly funded by NSERC, and was done while the author was a student at the University of Waterloo, visiting Laboratoire G-SCOP and the University of Liverpool.

Acknowledgements

We are very grateful to Sebastian Wild, who prevented us trying to reinvent perfect hashing.

Cite AsGet BibTex

Louis Esperet, Nathaniel Harms, and Viktor Zamaraev. Optimal Adjacency Labels for Subgraphs of Cartesian Products. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 57:1-57:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
https://doi.org/10.4230/LIPIcs.ICALP.2023.57

Abstract

For any hereditary graph class ℱ, we construct optimal adjacency labeling schemes for the classes of subgraphs and induced subgraphs of Cartesian products of graphs in ℱ. As a consequence, we show that, if ℱ admits efficient adjacency labels (or, equivalently, small induced-universal graphs) meeting the information-theoretic minimum, then the classes of subgraphs and induced subgraphs of Cartesian products of graphs in ℱ do too. Our proof uses ideas from randomized communication complexity and hashing, and improves upon recent results of Chepoi, Labourel, and Ratel [Journal of Graph Theory, 2020].

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Graph theory
  • Mathematics of computing → Combinatorics
Keywords
  • Adjacency labeling schemes
  • Cartesian product
  • Hypercubes

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References

  1. Bogdan Alecu, Vladimir E. Alekseev, Aistis Atminas, Vadim Lozin, and Viktor Zamaraev. Graph parameters, implicit representations and factorial properties. In submission, 2022. Google Scholar
  2. Bogdan Alecu, Aistis Atminas, and Vadim Lozin. Graph functionality. Journal of Combinatorial Theory, Series B, 147:139-158, 2021. Google Scholar
  3. Victor Chepoi, Arnaud Labourel, and Sébastien Ratel. On density of subgraphs of Cartesian products. Journal of Graph Theory, 93(1):64-87, 2020. Google Scholar
  4. Louis Esperet, Nathaniel Harms, and Andrey Kupavskii. Sketching distances in monotone graph classes. In International Conference on Randomization and Computation (RANDOM 2022), 2022. Google Scholar
  5. Ron L Graham. On primitive graphs and optimal vertex assignments. Annals of the New York academy of sciences, 175(1):170-186, 1970. Google Scholar
  6. Torben Hagerup and Torsten Tholey. Efficient minimal perfect hashing in nearly minimal space. In Annual Symposium on Theoretical Aspects of Computer Science (STACS 2001), pages 317-326. Springer, 2001. Google Scholar
  7. Lianna Hambardzumyan, Hamed Hatami, and Pooya Hatami. A counter-example to the probabilistic universal graph conjecture via randomized communication complexity. Discrete Applied Math., 2022. Google Scholar
  8. Nathaniel Harms. Universal communication, universal graphs, and graph labeling. In 11th Innovations in Theoretical Computer Science Conference (ITCS 2020), volume 151, page 33. Schloss Dagstuhl-Leibniz-Zentrum für Informatik, 2020. Google Scholar
  9. Nathaniel Harms. Adjacency labeling and sketching for induced subgraphs of the hypercube. https://cs.uwaterloo.ca/~nharms/downloads/hypercube_sketch.pdf, 2022.
  10. Nathaniel Harms, Sebastian Wild, and Viktor Zamaraev. Randomized communication and implicit graph representations. In 54th Annual Symposium on Theory of Computing (STOC 2022), 2022. Google Scholar
  11. Hamed Hatami and Pooya Hatami. The implicit graph conjecture is false. In 63rd IEEE Symposium on Foundations of Computer Science (FOCS 2022), 2022. Google Scholar
  12. David Haussler. Sphere packing numbers for subsets of the Boolean n-cube with bounded Vapnik-Chervonenkis dimension. Journal of Combinatorial Theory, Series A, 69(2):217-232, 1995. Google Scholar
  13. Sampath Kannan, Moni Naor, and Steven Rudich. Implicit representation of graphs. SIAM Journal on Discrete Mathematics, 5(4):596-603, 1992. Google Scholar
  14. Kurt Mehlhorn. Data Structures and Algorithms 1 Sorting and Searching. Monographs in Theoretical Computer Science. An EATCS Series, 1. Springer Berlin Heidelberg, Berlin, Heidelberg, 1st ed. 1984. edition, 1984. Google Scholar
  15. John H Muller. Local structure in graph classes, 1989. Google Scholar
  16. Edward R Scheinerman. Local representations using very short labels. Discrete mathematics, 203(1-3):287-290, 1999. Google Scholar
  17. Jeremy P Spinrad. Efficient graph representations. American Mathematical Society, 2003. Google Scholar
  18. Andrew Chi-Chih Yao. On the power of quantum fingerprinting. In Proceedings of the Thirty-Fifth Annual ACM Symposium on Theory of Computing (STOC), pages 77-81, 2003. Google Scholar
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