Abstract
We show how to preprocess a weighted undirected n-vertex planar graph in Õ(n4/3) time, such that the distance between any pair of vertices can then be reported in Õ(1) time. This improves the previous Õ(n3/2) 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].
| Original language | English |
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| Title of host publication | 52nd International Colloquium on Automata, Languages, and Programming, ICALP 2025 |
| Editors | Keren Censor-Hillel, Fabrizio Grandoni, Joel Ouaknine, Gabriele Puppis |
| Publisher | Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing |
| ISBN (Electronic) | 9783959773720 |
| DOIs | |
| State | Published - 30 Jun 2025 |
| Event | 52nd EATCS International Colloquium on Automata, Languages, and Programming, ICALP 2025 - Aarhus, Denmark Duration: 8 Jul 2025 → 11 Jul 2025 |
Publication series
| Name | Leibniz International Proceedings in Informatics, LIPIcs |
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| Volume | 334 |
| ISSN (Print) | 1868-8969 |
Conference
| Conference | 52nd EATCS International Colloquium on Automata, Languages, and Programming, ICALP 2025 |
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| Country/Territory | Denmark |
| City | Aarhus |
| Period | 8/07/25 → 11/07/25 |
Bibliographical note
Publisher Copyright:© Itai Boneh, Shay Golan, Shay Mozes, Daniel Prigan, and Oren Weimann.
Keywords
- Construction Time
- Distance Oracle
- Planar Graph
ASJC Scopus subject areas
- Software