Dynamic Light Spanners in Doubling Metrics
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866917360129015808 |
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| author | Bhore, Sujoy Conroy, Jonathan Filtser, Arnold |
| author_facet | Bhore, Sujoy Conroy, Jonathan Filtser, Arnold |
| contents | A $t$-spanner of a point set $X$ in a metric space $(\mathcal{X}, δ)$ is a graph $G$ with vertex set $P$ such that, for any pair of points $u,v \in X$, the distance between $u$ and $v$ in $G$ is at most $t$ times $δ(u,v)$. We study the problem of maintaining a spanner for a dynamic point set $X$ -- that is, when $X$ undergoes a sequence of insertions and deletions -- in a metric space of constant doubling dimension. For any constant $\varepsilon>0$, we maintain a $(1+\varepsilon)$-spanner of $P$ whose total weight remains within a constant factor of the weight of the minimum spanning tree of $X$. Each update (insertion or deletion) can be performed in $\operatorname{poly}(\log Φ)$ time, where $Φ$ denotes the aspect ratio of $X$. Prior to our work, no efficient dynamic algorithm for maintaining a light-weight spanner was known even for point sets in low-dimensional Euclidean space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_23490 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Dynamic Light Spanners in Doubling Metrics Bhore, Sujoy Conroy, Jonathan Filtser, Arnold Computational Geometry Data Structures and Algorithms A $t$-spanner of a point set $X$ in a metric space $(\mathcal{X}, δ)$ is a graph $G$ with vertex set $P$ such that, for any pair of points $u,v \in X$, the distance between $u$ and $v$ in $G$ is at most $t$ times $δ(u,v)$. We study the problem of maintaining a spanner for a dynamic point set $X$ -- that is, when $X$ undergoes a sequence of insertions and deletions -- in a metric space of constant doubling dimension. For any constant $\varepsilon>0$, we maintain a $(1+\varepsilon)$-spanner of $P$ whose total weight remains within a constant factor of the weight of the minimum spanning tree of $X$. Each update (insertion or deletion) can be performed in $\operatorname{poly}(\log Φ)$ time, where $Φ$ denotes the aspect ratio of $X$. Prior to our work, no efficient dynamic algorithm for maintaining a light-weight spanner was known even for point sets in low-dimensional Euclidean space. |
| title | Dynamic Light Spanners in Doubling Metrics |
| topic | Computational Geometry Data Structures and Algorithms |
| url | https://arxiv.org/abs/2603.23490 |