TY - GEN

T1 - A Near-Optimal Offline Algorithm for Dynamic All-Pairs Shortest Paths in Planar Digraphs

AU - Das, Debarati

AU - Gutenberg, Maximilian Probst

AU - Wulff-Nilsen, Christian

N1 - Publisher Copyright:
Copyright © 2022 by SIAM.

PY - 2022

Y1 - 2022

N2 - In the planar, dynamic All-Pairs Shortest Paths (APSP) problem, a planar, weighted digraph G undergoes a sequence of edge weight updates and the goal is to maintain a data structure on G, that can quickly answer distance queries between any two vertices x,y ? V(G). The currently best algorithms [FOCS'01, SODA'05] for this problem require Õ(n2/3) worst-case update and query time, while conditional lower bounds [FOCS'16] show that either update or query time is needed1. In this article, we present the first algorithm with near-optimal worst-case update and query time for the offline setting, where the update sequence is given initially. This result is obtained by giving the first offline dynamic algorithm for maintaining dense distance graphs (DDGs) faster than recomputing from scratch after each update. Further, we also present an online algorithm for the incremental APSP problem with worst-case update/query time. This allows us to reduce the online dynamic APSP problem to the online decremental APSP problem, which constitutes partial progress even for the online version of this notorious problem.

AB - In the planar, dynamic All-Pairs Shortest Paths (APSP) problem, a planar, weighted digraph G undergoes a sequence of edge weight updates and the goal is to maintain a data structure on G, that can quickly answer distance queries between any two vertices x,y ? V(G). The currently best algorithms [FOCS'01, SODA'05] for this problem require Õ(n2/3) worst-case update and query time, while conditional lower bounds [FOCS'16] show that either update or query time is needed1. In this article, we present the first algorithm with near-optimal worst-case update and query time for the offline setting, where the update sequence is given initially. This result is obtained by giving the first offline dynamic algorithm for maintaining dense distance graphs (DDGs) faster than recomputing from scratch after each update. Further, we also present an online algorithm for the incremental APSP problem with worst-case update/query time. This allows us to reduce the online dynamic APSP problem to the online decremental APSP problem, which constitutes partial progress even for the online version of this notorious problem.

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M3 - Conference contribution

AN - SCOPUS:85127299237

T3 - Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

SP - 3482

EP - 3495

BT - ACM-SIAM Symposium on Discrete Algorithms, SODA 2022

PB - Association for Computing Machinery

T2 - 33rd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2022

Y2 - 9 January 2022 through 12 January 2022

ER -