Dynamic Deterministic Constant-Approximate Distance Oracles with n^ Worst-Case Update Time
We present a new distance oracle in the fully dynamic setting: given a weighted undirected graph G = (V, E) with n vertices undergoing both edge insertions and deletions, and an arbitrary parameter \epsilon\in[1/\log^{c}n, 1 where c > 0 is a small constant, we can deterministically maintain a dat...
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| Vydané v: | Proceedings / annual Symposium on Foundations of Computer Science s. 2033 - 2044 |
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| Hlavní autori: | , , |
| Médium: | Konferenčný príspevok.. |
| Jazyk: | English |
| Vydavateľské údaje: |
IEEE
27.10.2024
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| Predmet: | |
| ISSN: | 2575-8454 |
| On-line prístup: | Získať plný text |
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| Shrnutí: | We present a new distance oracle in the fully dynamic setting: given a weighted undirected graph G = (V, E) with n vertices undergoing both edge insertions and deletions, and an arbitrary parameter \epsilon\in[1/\log^{c}n, 1 where c > 0 is a small constant, we can deterministically maintain a data structure with O(n^{\epsilon}) worst-case update time that, given any pair of vertices (u, v), returns a 2^{\text{poly}(1/\epsilon)} -approximate distance between u and v in poly(1/E) log log n query time. Our algorithm significantly advances the state-of-the-art in two aspects, both for fully dynamic algorithms and even decremental algorithms. First, no existing algorithm with worst-case update time guarantees a o( n )-approximation while also achieving an n 2-Ω(1) update and n^{o(1)} query time, while our algorithm offers a constant O_{\epsilon}(1) -approximation with O(n^{\epsilon}) update time and o_{\epsilon} (log log n) query time. Second, even if amortized update time is allowed, it is the first deterministic constant-approximation algorithm with n^{1-\Omega(1)} update and query time. The best result in this direction is the recent deterministic distance oracle by Chuzhoy and Zhang [STOC 2023] which achieves an approxi- mation of (log log n)^{2^{O (1 / \epsilon^3)}} with amortized update time of O(n^{\epsilon)} and query time of 2^{\mathrm{p}\circ 1\mathrm{y}(1/\epsilon)}\log n log log n. We obtain the result by dynamizing tools related to length- constrained expanders [Haeupler-Racke-Ghaffari, STOC 2022; Haeupler-Hershkowitz-Tan, FOCS 2024]. Our technique com- pletely bypasses the 40-year-old Even-Shiloach tree, which has remained the most pervasive tool in the area but is inherently amortized. |
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| ISSN: | 2575-8454 |
| DOI: | 10.1109/FOCS61266.2024.00121 |