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Distance Labeling for Families of Cycles

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SOFSEM 2024: Theory and Practice of Computer Science (SOFSEM 2024)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14519))

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Abstract

For an arbitrary finite family of graphs, the distance labeling problem asks to assign labels to all nodes of every graph in the family in a way that allows one to recover the distance between any two nodes of any graph from their labels. The main goal is to minimize the number of unique labels used. We study this problem for the families \(\mathcal {C}_n\) consisting of cycles of all lengths between 3 and n. We observe that the exact solution for directed cycles is straightforward and focus on the undirected case. We design a labeling scheme requiring \(\frac{n\sqrt{n}}{\sqrt{6}}+O(n)\) labels, which is almost twice less than is required by the earlier known scheme. Using the computer search, we find an optimal labeling for each \(n\le 17\), showing that our scheme gives the results that are very close to the optimum.

The first author is supported by the grant MPM no. ERC 683064 under the EU’s Horizon 2020 Research and Innovation Programme and by the State of Israel through the Center for Absorption in Science of the Ministry of Aliyah and Immigration.

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Notes

  1. 1.

    Throughout the paper, \(\log \) stands for the binary logarithm.

  2. 2.

    E. Porat, private communication.

  3. 3.

    S. Alstrup, private communication.

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Acknowledgements

We are grateful to E. Porat for introducing the distance labeling problem to us. Our special thanks to A. Safronov for the assistance in computational experiments.

Author information

Authors and Affiliations

  1. Bar Ilan University, Ramat Gan, Israel

    Arseny M. Shur

  2. SPGuide Online School in Algorithms, Karmiel, Israel

    Mikhail Rubinchik

Authors
  1. Arseny M. Shur
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  2. Mikhail Rubinchik
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Correspondence to Arseny M. Shur .

Editor information

Editors and Affiliations

  1. University of Trier, Trier, Germany

    Henning Fernau

  2. UNSW Sydney, Sydney, NSW, Australia

    Serge Gaspers

  3. CNRS and University of Bordeaux, Talence, France

    Ralf Klasing

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Shur, A.M., Rubinchik, M. (2024). Distance Labeling for Families of Cycles. In: Fernau, H., Gaspers, S., Klasing, R. (eds) SOFSEM 2024: Theory and Practice of Computer Science. SOFSEM 2024. Lecture Notes in Computer Science, vol 14519. Springer, Cham. https://doi.org/10.1007/978-3-031-52113-3_33

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  • DOI: https://doi.org/10.1007/978-3-031-52113-3_33

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-52112-6

  • Online ISBN: 978-3-031-52113-3

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