Almost Optimal Exact Distance Oracles for Planar Graphs

Panagiotis Charalampopoulos, Paweł Gawrychowski, Yaowei Long, Shay Mozes, Seth Pettie, Oren Weimann, Christian Wulff-Nilsen

Research output: Contribution to journalArticlepeer-review


We consider the problem of preprocessing a weighted directed planar graph in order to quickly answer exact distance queries. The main tension in this problem is between space S and query time Q, and since the mid-1990s all results had polynomial time-space tradeoffs, e.g., Q = ∼θ(n/g√S) or Q = ∼θ(n5/2/S3/2). In this article we show that there is no polynomial tradeoff between time and space and that it is possible to simultaneously achieve almost optimal space n1+o(1) and almost optimal query time no(1). More precisely, we achieve the following space-time tradeoffs:n1+o(1) space and log2+o(1) n query time,n log2+o(1) n space and no(1) query time,n4/3+o(1) space and log1+o(1) n query time.We reduce a distance query to a variety of point location problems in additively weighted Voronoi diagrams and develop new algorithms for the point location problem itself using several partially persistent dynamic tree data structures.

Original languageEnglish
Article number12
JournalJournal of the ACM
Issue number2
StatePublished - 25 Mar 2023

Bibliographical note

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© 2023 Copyright held by the owner/author(s). Publication rights licensed to ACM.


  • Planar graphs
  • Voronoi diagrams
  • distance oracles
  • persistent data structures

ASJC Scopus subject areas

  • Software
  • Control and Systems Engineering
  • Information Systems
  • Hardware and Architecture
  • Artificial Intelligence


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