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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.17262 |
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| _version_ | 1866915563476877312 |
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| author | Qi, Chuhan |
| author_facet | Qi, Chuhan |
| contents | Additive spanners are fundamental graph structures with wide applications in network design, graph sparsification, and distance approximation. In particular, a $4$-additive spanner is a subgraph that preserves all pairwise distances up to an additive error of $4$. In this paper, we present a new deterministic algorithm for constructing $4$-additive spanners that matches the best known edge bound of $\tilde{O}(n^{7/5})$ (up to polylogarithmic factors), while improving the running time to $\tilde{O}(\min\{mn^{3/5}, n^{11/5}\})$, compared to the previous $\tilde{O}(mn^{3/5})$ randomized construction. Our algorithm is not only faster in the dense regime but also fully deterministic, conceptually simpler, and easier to implement and analyze. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_17262 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Finding 4-Additive Spanners: Faster, Stronger, and Simpler Qi, Chuhan Data Structures and Algorithms Additive spanners are fundamental graph structures with wide applications in network design, graph sparsification, and distance approximation. In particular, a $4$-additive spanner is a subgraph that preserves all pairwise distances up to an additive error of $4$. In this paper, we present a new deterministic algorithm for constructing $4$-additive spanners that matches the best known edge bound of $\tilde{O}(n^{7/5})$ (up to polylogarithmic factors), while improving the running time to $\tilde{O}(\min\{mn^{3/5}, n^{11/5}\})$, compared to the previous $\tilde{O}(mn^{3/5})$ randomized construction. Our algorithm is not only faster in the dense regime but also fully deterministic, conceptually simpler, and easier to implement and analyze. |
| title | Finding 4-Additive Spanners: Faster, Stronger, and Simpler |
| topic | Data Structures and Algorithms |
| url | https://arxiv.org/abs/2510.17262 |