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- W4298862706 abstract "We address the problem of replicating a Voronoi diagram $V(S)$ of a planar point set $S$ by making proximity queries, which are of three possible (in decreasing order of information content): 1. the exact location of the nearest site(s) in $S$; 2. the distance to and label(s) of the nearest site(s) in $S$; 3. a unique label for every nearest site in $S$. We provide algorithms showing how queries of Type 1 and Type 2 allow an exact cloning of $V(S)$ with $O(n)$ queries and $O(n log^2 n)$ processing time. We also prove that queries of Type 3 can never exactly clone $V(S)$, but we show that with $O(n logfrac{1}{epsilon})$ queries we can construct an $epsilon$-approximate cloning of $V(S)$. In addition to showing the limits of nearest-neighbor database security, our methods also provide one of the first natural algorithmic applications of retroactive data structures." @default.
- W4298862706 created "2022-10-02" @default.
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- W4298862706 date "2010-06-09" @default.
- W4298862706 modified "2023-09-27" @default.
- W4298862706 title "Cloning Voronoi Diagrams via Retroactive Data Structures" @default.
- W4298862706 doi "https://doi.org/10.48550/arxiv.1006.1921" @default.
- W4298862706 hasPublicationYear "2010" @default.
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