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  "path": "/abs/2603.23490v1",
  "publishedAt": "2026-03-25T00:00:00.000Z",
  "site": "https://arxiv.org",
  "tags": [
    "Sujoy Bhore",
    "Jonathan Conroy",
    "Arnold Filtser"
  ],
  "textContent": "**Authors:** Sujoy Bhore, Jonathan Conroy, Arnold Filtser\n\nA $t$-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"
}