Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Top-$k$ Weighted SUM Aggregate Nearest and Farthest Neighbors in the
  $L_1$ Plane   In this paper, we study top-$k$ aggregate (or group) nearest neighbor queries
using the weighted SUM operator under the $L_1$ metric in the plane. Given a
set $P$ of $n$ points, for any query consisting of a set $Q$ of $m$ weighted
points and an integer $k$, $ 1 \le k \le n$, the top-$k$ aggregate nearest
neighbor query asks for the $k$ points of $P$ whose aggregate distances to $Q$
are the smallest, where the aggregate distance of each point $p$ of $P$ to $Q$
is the sum of the weighted distances from $p$ to all points of $Q$. We build an
$O(n\log n\log\log n)$-size data structure in $O(n\log n \log\log n)$ time,
such that each top-$k$ query can be answered in $O(m\log m+(k+m)\log^2 n)$
time. We also obtain other results with trade-off between preprocessing and
query. Even for the special case where $k=1$, our results are better than the
previously best method (in PODS 2012), which requires $O(n\log^2 n)$
preprocessing time, $O(n\log^2 n)$ space, and $O(m^2\log^3 n)$ query time. In
addition, for the one-dimensional version of this problem, our approach can
build an $O(n)$-size data structure in $O(n\log n)$ time that can support
$O(\min\{k,\log m\}\cdot m+k+\log n)$ time queries. Further, we extend our
techniques to the top-$k$ aggregate farthest neighbor queries, with the same
bounds.

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The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
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The categories of this paper are: alg-geom
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The categories of this paper are: chem-ph
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The categories of this paper are: eess
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The categories of this paper are: cmp-lg
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-lat
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The categories of this paper are: nlin
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The categories of this paper are: funct-an
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The categories of this paper are: hep-ex
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The categories of this paper are: math-ph
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The categories of this paper are: adap-org
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The categories of this paper are: bayes-an