Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Note on Indexing Point Sets for Approximate Bottleneck Distance
  Queries   The {\em bottleneck distance} is a natural measure of the distance between
two finite point sets of equal cardinality, defined as the minimum over all
bijections between the point sets of the maximum distance between any pair of
points put in correspondence by the bijection. In this work, we consider the
problem of building a data structure $\mathbb{D}$ that indexes a collection of
$m$ planar point sets (of varying sizes) and supports nearest bottleneck
distance queries: given a query point set $Q$ of size $n$, we would like to
find the point set(s) $P \in \mathbb{D}$ of size $n$ that are closest in terms
of bottleneck distance. Without loss of generality, we assume that all point
sets belong to the unit box $[0,1]^2$ in the plane and focus on the $L_\infty$
norm, although the techniques can also be used for other norms. The main
contribution is a {\em trie}-based data structure finds a $6$-approximate
nearest neighbor in $O(-\lg(d_B(\mathbb{D},Q)) n)$ time, where
$d_B(\mathbb{D},Q)$ is the minimum bottleneck distance from $Q$ to any point
set in $\mathbb{D}$.

16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
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The categories of this paper are: eess
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The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
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The categories of this paper are: econ
32
The categories of this paper are: atom-ph
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The categories of this paper are: math-ph