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• W2893502149 abstract "For any constant $d$ and parameter $varepsilon > 0$, we show the existence of (roughly) $1/varepsilon^d$ orderings on the unit cube $[0,1)^d$, such that any two points $p,qin [0,1)^d$ that are under the Euclidean metric are close together in one of these linear orderings in the following sense: the only points that could lie between $p$ and $q$ in the ordering are points with Euclidean distance at most $varepsilon| p - q |$ from $p$ or $q$. These orderings are extensions of the $mathcal{Z}$-order, and they can be efficiently computed. Functionally, the orderings can be thought of as a replacement to quadtrees and related structures (like well-separated pair decompositions). We use such orderings to obtain surprisingly simple algorithms for a number of basic problems in low-dimensional computational geometry, including (i) dynamic approximate bichromatic closest pair, (ii) dynamic spanners, (iii) dynamic approximate minimum spanning trees, (iv) static and dynamic fault-tolerant spanners, and (v) approximate nearest neighbor search." @default.
• W2893502149 created "2018-10-05" @default.
• W2893502149 creator A5012548113 @default.
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• W2893502149 date "2018-09-28" @default.
• W2893502149 modified "2023-09-27" @default.
• W2893502149 title "On Locality-Sensitive Orderings and their Applications" @default.
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