Abstract
We study the fully-dynamic all-pair shortest paths (APSP) problem on planar graphs: given an n-vertex} planar graph G=(V, E) undergoing edge insertions and deletions, the goal is to efficiently process these updates and support distance and shortest path queries. We give a (1+ϵ)-approximate} dynamic algorithm that supports edge updates and distance queries in no(1) time, for any 1/poly(log n) < ϵ < 1. Our result is a significant improvement over the best previously known bound of Õ(√{n}) on update and query time due to [Abraham, Chechik, and Gavoille, STOC '12], and bypasses a Ω(√{n}) conditional lower-bound on update and query time for exact fully dynamic planar APSP [Abboud and Dahlgaard, FOCS '16]. The main technical contribution behind our result is to dynamize the planar emulator construction due to [Chang, Krauthgamer, Tan, STOC '22].
| Original language | English |
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| Title of host publication | Proceedings - 2024 IEEE 65th Annual Symposium on Foundations of Computer Science, FOCS 2024 |
| Publisher | IEEE Computer Society |
| Pages | 2078-2098 |
| Number of pages | 21 |
| ISBN (Electronic) | 9798331516741 |
| DOIs | |
| State | Published - 2024 |
| Event | 65th IEEE Annual Symposium on Foundations of Computer Science, FOCS 2024 - Chicago, United States Duration: 27 Oct 2024 → 30 Oct 2024 |
Publication series
| Name | Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS |
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| ISSN (Print) | 0272-5428 |
Conference
| Conference | 65th IEEE Annual Symposium on Foundations of Computer Science, FOCS 2024 |
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| Country/Territory | United States |
| City | Chicago |
| Period | 27/10/24 → 30/10/24 |
Bibliographical note
Publisher Copyright:© 2024 IEEE.
Keywords
- Distance Emulator
- Distance Oracles
- Dynamic Data Structure
- Planar Graph