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  "path": "/abs/2602.06633v1",
  "publishedAt": "2026-02-09T01:00:00.000Z",
  "site": "https://arxiv.org",
  "tags": [
    "Jeff Giliberti",
    "Sariel Har-Peled Jonas Sauer",
    "Ali Vakilian"
  ],
  "textContent": "**Authors:** Jeff Giliberti, Sariel Har-Peled Jonas Sauer, Ali Vakilian\n\n$\\renewcommand{\\Re}{\\mathbb{R}}$Recent work showed how to construct nearest-neighbor graphs of linear size, on a given set $P$ of $n$ points in $\\Re^d$, such that one can answer approximate nearest-neighbor queries in logarithmic time in the spread. Unfortunately, the spread might be unbounded in $n$, and an interesting theoretical question is how to remove the dependency on the spread. Here, we show how to construct an external linear-size data structure that, combined with the linear-size graph, allows us to answer ANN queries in logarithmic time in $n$.",
  "title": "Graph-Based Nearest-Neighbor Search without the Spread"
}