A Simple Dynamic Spanner via APSP
<|reference_start|>A Simple Dynamic Spanner via APSP: We give a simple algorithm for maintaining a $n^{o(1)}$-approximate spanner $H$ of a graph $G$ with $n$ vertices as $G$ receives edge updates by reduction to the dynamic All-Pairs Shortest Paths (APSP) problem. Given an initially empty graph $G$, our algorithm processes $m$ insertions and $n$ deletions in total time $m^{1 + o(1)}$ and maintains an initially empty spanner $H$ with total recourse $n^{1 + o(1)}$. When the number of insertions is much larger than the number of deletions, this notably yields recourse sub-linear in the total number of updates.   Our algorithm only has a single $O(\log n)$ factor overhead in runtime and approximation compared to the underlying APSP data structure. Therefore, future improvements for APSP will directly yield an improved dynamic spanner.<|reference_end|>
@article{kyng2024a,
    title={A Simple Dynamic Spanner via APSP},
    author={Rasmus Kyng, Simon Meierhans, Gernot Z"ocklein},
    journal={arXiv preprint arXiv:2408.11368},
    year={2024},
    archivePrefix={arXiv},
    eprint={2408.11368},
    primaryClass={cs.DS}
}