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Truly Subquadratic Exact Distance Oracles with Constant Query Time for Planar Graphs

Authors Viktor Fredslund-Hansen , Shay Mozes , Christian Wulff-Nilsen

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ACM Subject Classification
  • Theory of computation → Data structures design and analysis
  • Theory of computation → Shortest paths
  • Mathematics of computing → Graph algorithms
Keywords
  • distance oracle
  • planar graph
  • shortest paths
  • subquadratic

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Abstract

We present a truly subquadratic size distance oracle for reporting, in constant time, the exact shortest-path distance between any pair of vertices of an undirected, unweighted planar graph G. For any ε > 0, our distance oracle requires O(n^{5/3+ε}) space and is capable of answering shortest-path distance queries exactly for any pair of vertices of G in worst-case time O(log (1/ε)). Previously no truly sub-quadratic size distance oracles with constant query time for answering exact shortest paths distance queries existed.

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Viktor Fredslund-Hansen, Shay Mozes, and Christian Wulff-Nilsen. Truly Subquadratic Exact Distance Oracles with Constant Query Time for Planar Graphs. In 32nd International Symposium on Algorithms and Computation (ISAAC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 212, pp. 25:1-25:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021) https://doi.org/10.4230/LIPIcs.ISAAC.2021.25

Author Details

Viktor Fredslund-Hansen
  • Department of Computer Science, University of Copenhagen, Denmark
Shay Mozes
  • The Interdisciplinary Center, Herzliya, Israel
Christian Wulff-Nilsen
  • Department of Computer Science, University of Copenhagen, Denmark

Funding

  • Mozes, Shay: Partially supported by Israel Science Foundation grant No. 592/17.
  • Wulff-Nilsen, Christian: This research is supported by the Starting Grant 7027-00050B from the Independent Research Fund Denmark under the Sapere Aude research career programme and by Basic Algorithms Research Copenhagen (BARC).

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