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Faster Construction of a Planar Distance Oracle with Õ(1) Query Time

Authors Itai Boneh , Shay Golan , Shay Mozes , Daniel Prigan , Oren Weimann

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  • Theory of computation → Data structures design and analysis
Keywords
  • Distance Oracle
  • Planar Graph
  • Construction Time

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Abstract

We show how to preprocess a weighted undirected n-vertex planar graph in Õ(n^{4/3}) time, such that the distance between any pair of vertices can then be reported in Õ(1) time. This improves the previous Õ(n^{3/2}) preprocessing time [JACM'23].
Our main technical contribution is a near optimal construction of additively weighted Voronoi diagrams in undirected planar graphs. Namely, given a planar graph G and a face f, we show that one can preprocess G in Õ(n) time such that given any weight assignment to the vertices of f one can construct the additively weighted Voronoi diagram of f in near optimal Õ(|f|) time. This improves the Õ(√{n|f|}) construction time of [JACM'23].

Cite As Get BibTex

Itai Boneh, Shay Golan, Shay Mozes, Daniel Prigan, and Oren Weimann. Faster Construction of a Planar Distance Oracle with Õ(1) Query Time. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 33:1-33:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ICALP.2025.33

Author Details

Itai Boneh
  • University of Haifa, Israel
  • Reichman University, Herzliya, Israel
Shay Golan
  • University of Haifa, Israel
  • Reichman University, Herzliya, Israel
Shay Mozes
  • Reichman University, Herzliya, Israel
Daniel Prigan
  • Reichman University, Herzliya, Israel
Oren Weimann
  • University of Haifa, Israel

Funding

Israel Science Foundation grant 810/21.

References

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