Super-Logarithmic Lower Bounds for Dynamic Graph Problems

In this work, we prove a \tilde{\Omega}(\lg^{3/2} n) unconditional lower bound on the maximum of the query time and update time for dynamic data structures supporting reachability queries in n-node directed acyclic graphs under edge insertions. This is the first super-logarithmic lower bound for any...

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Bibliographic Details
Published in:Proceedings / annual Symposium on Foundations of Computer Science pp. 1589 - 1604
Main Authors: Larsen, Kasper Green, Yu, Huacheng
Format: Conference Proceeding
Language:English
Published: IEEE 06.11.2023
Subjects:
cell-probe model
Computational modeling
Computer science
data structure lower bounds
Data structures
Directed acyclic graph
dynamic graph algorithms
dynamic reachability
Heuristic algorithms
ISSN:2575-8454
Online Access:Get full text
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Summary:In this work, we prove a \tilde{\Omega}(\lg^{3/2} n) unconditional lower bound on the maximum of the query time and update time for dynamic data structures supporting reachability queries in n-node directed acyclic graphs under edge insertions. This is the first super-logarithmic lower bound for any natural graph problem. In proving the lower bound, we also make novel contributions to the state-of-the-art data structure lower bound techniques that we hope may lead to further progress in proving lower bounds.
ISSN:2575-8454
DOI:10.1109/FOCS57990.2023.00096