## Abstract

Designing approximate all-pairs distance oracles in the fully dynamic setting is one of the central problems in dynamic graph algorithms. Despite extensive research on this topic, the first result breaking the O(√n) barrier on the update time for any non-trivial approximation was introduced only recently by Forster, Goranci and Henzinger [SODA’21] who achieved m
^{1/ρ+o(1)} amortized update time with a O(log n)
^{3ρ−2} factor in the approximation ratio, for any parameter ρ ≥ 1. In this paper, we give the first constant-stretch fully dynamic distance oracle with small polynomial update and query time. Prior work required either at least a poly-logarithmic approximation or much larger update time. Our result gives a more fine-grained trade-off between stretch and update time, for instance we can achieve constant stretch of O(1/ρ2)
^{4/ρ} in amortized update time Õ(n
^{ρ}), and query time Õ(n
^{ρ/8}) for any constant parameter 0 < ρ < 1. Our algorithm is randomized and assumes an oblivious adversary. A core technical idea underlying our construction is to design a black-box reduction from decremental approximate hub-labeling schemes to fully dynamic distance oracles, which may be of independent interest. We then apply this reduction repeatedly to an existing decremental algorithm to bootstrap our fully dynamic solution.

Original language | English |
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Title of host publication | 31st Annual European Symposium on Algorithms, ESA 2023 |

Editors | Inge Li Gortz, Martin Farach-Colton, Simon J. Puglisi, Grzegorz Herman |

ISBN (Electronic) | 9783959772952 |

DOIs | |

Publication status | Published - 1 Sep 2023 |

## Austrian Fields of Science 2012

- 102031 Theoretical computer science

## Keywords

- Distance Oracles
- Dynamic graph algorithms
- Shortest Paths