TY - GEN
T1 - Near-Optimal (1+ϵ)-Approximate Fully-Dynamic All-Pairs Shortest Paths in Planar Graphs
AU - Filtser, Arnold
AU - Goranci, Gramoz
AU - Patel, Neel
AU - Gutenberg, Maximilian Probst
N1 - Publisher Copyright: © 2024 IEEE.
PY - 2024/1/1
Y1 - 2024/1/1
N2 - 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].
AB - 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].
KW - Distance Emulator
KW - Distance Oracles
KW - Dynamic Data Structure
KW - Planar Graph
UR - http://www.scopus.com/inward/record.url?scp=85213011895&partnerID=8YFLogxK
U2 - 10.1109/FOCS61266.2024.00124
DO - 10.1109/FOCS61266.2024.00124
M3 - منشور من مؤتمر
T3 - Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
SP - 2078
EP - 2098
BT - Proceedings - 2024 IEEE 65th Annual Symposium on Foundations of Computer Science, FOCS 2024
PB - IEEE Computer Society
T2 - 65th IEEE Annual Symposium on Foundations of Computer Science, FOCS 2024
Y2 - 27 October 2024 through 30 October 2024
ER -