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- W2897594638 abstract "The {em bottleneck distance} is a natural measure of the distance between two finite point sets of equal cardinality. In this work, we consider the problem of indexing a set of $m$ planar point sets (of varying sizes) to create a database $D$ that supports nearest bottleneck distance queries: given a query point set $Q$ of size $n$, the point sets $P in D$ that are closest in terms of bottleneck distance are returned. Without loss of generality, we assume that all point sets belong to the unit box $[0,1]^2$ in the plane. The main contribution of this work is a {em trie}-based data structure that is space efficient and supports $8$-approximate nearest bottleneck queries in $O(-lg(d_B(D,Q)) min(m,{10}^n) n lg^3 n)$ time, where $d_B(D,Q)$ is the minimum bottleneck distance from $Q$ to any point set in $D$. A direct consequence, of independent interest, is a simple $O(-lg(d_B(P,Q)) n lg^3 n)$ time algorithm to $2 sqrt{2}$-approximate $d_B(P,Q)$, for any two point sets $P$ and $Q$. Finally, the querying algorithm proposed is easily adapted to support nearest subset and superset queries." @default.
- W2897594638 created "2018-10-26" @default.
- W2897594638 creator A5084888509 @default.
- W2897594638 date "2018-10-22" @default.
- W2897594638 modified "2023-09-27" @default.
- W2897594638 title "Indexing Point Sets for Approximate Bottleneck Distance Queries" @default.
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