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Algorithms for Distance Problems in Continuous Graphs

Authors Sergio Cabello , Delia Garijo , Antonia Kalb , Fabian Klute , Irene Parada , Rodrigo I. Silveira

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Subject Classification

ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
Keywords
  • diameter
  • mean distance
  • continuous graph
  • treewidth
  • planar graph

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Abstract

We study the problem of computing the diameter and the mean distance of a continuous graph, i.e., a connected graph where all points along the edges, instead of only the vertices, must be taken into account. It is known that for continuous graphs with m edges these values can be computed in roughly O(m²) time. In this paper, we use geometric techniques to obtain subquadratic time algorithms to compute the diameter and the mean distance of a continuous graph for two well-established classes of sparse graphs. We show that the diameter and the mean distance of a continuous graph of treewidth at most k can be computed in O(n log^O(k) n) time, where n is the number of vertices in the graph. We also show that computing the diameter and mean distance of a continuous planar graph with n vertices and F faces takes O(n F log n) time.

Cite As Get BibTex

Sergio Cabello, Delia Garijo, Antonia Kalb, Fabian Klute, Irene Parada, and Rodrigo I. Silveira. Algorithms for Distance Problems in Continuous Graphs. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 13:1-13:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.WADS.2025.13

Author Details

Sergio Cabello
  • Faculty of Mathematics and Physics, University of Ljubljana, Slovenia
  • Institute of Mathematics, Physics and Mechanics, Ljubljana, Slovenia
Delia Garijo
  • University of Seville, Spain
Antonia Kalb
  • Technical University of Dortmund, Germany
Fabian Klute
  • Universitat Politècnica de Catalunya, Barcelona, Spain
Irene Parada
  • Universitat Politècnica de Catalunya, Barcelona, Spain
Rodrigo I. Silveira
  • Universitat Politècnica de Catalunya, Barcelona, Spain

Funding

  • Cabello, Sergio: Funded in part by the Slovenian Research and Innovation Agency (P1-0297, N1-0218, N1-0285). Funded in part by the European Union (ERC, KARST, project number 101071836). Views and opinions expressed are however those of the authors only and do not necessarily reflect those of the European Union or the European Research Council. Neither the European Union nor the granting authority can be held responsible for them.
  • Garijo, Delia: Partially supported by grants PID2019-104129GB-I00 and PID2023-150725NB-I00 funded by MICIU/AEI/10.13039/501100011033.
  • Klute, Fabian: Partially supported by grants PID2019-104129GB-I00 and PID2023-150725NB-I00 funded by MICIU/AEI/10.13039/501100011033.
  • Parada, Irene: Serra Húnter Fellow. Partially supported by grants PID2019-104129GB-I00 and PID2023-150725NB-I00 funded by MICIU/AEI/10.13039/501100011033.
  • Silveira, Rodrigo I.: Partially supported by grants PID2019-104129GB-I00 and PID2023-150725NB-I00 funded by MICIU/AEI/ 10.13039/501100011033.

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