Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Simultaneous Nearest Neighbor Search   Motivated by applications in computer vision and databases, we introduce and
study the Simultaneous Nearest Neighbor Search (SNN) problem. Given a set of
data points, the goal of SNN is to design a data structure that, given a
collection of queries, finds a collection of close points that are compatible
with each other. Formally, we are given $k$ query points $Q=q_1,\cdots,q_k$,
and a compatibility graph $G$ with vertices in $Q$, and the goal is to return
data points $p_1,\cdots,p_k$ that minimize (i) the weighted sum of the
distances from $q_i$ to $p_i$ and (ii) the weighted sum, over all edges $(i,j)$
in the compatibility graph $G$, of the distances between $p_i$ and $p_j$. The
problem has several applications, where one wants to return a set of consistent
answers to multiple related queries. This generalizes well-studied
computational problems, including NN, Aggregate NN and the 0-extension problem.
  In this paper we propose and analyze the following general two-step method
for designing efficient data structures for SNN. In the first step, for each
query point $q_i$ we find its (approximate) nearest neighbor point $\hat{p}_i$;
this can be done efficiently using existing approximate nearest neighbor
structures. In the second step, we solve an off-line optimization problem over
sets $q_1,\cdots,q_k$ and $\hat{p}_1,\cdots,\hat{p}_k$; this can be done
efficiently given that $k$ is much smaller than $n$. Even though
$\hat{p}_1,\cdots,\hat{p}_k$ might not constitute the optimal answers to
queries $q_1,\cdots,q_k$, we show that, for the unweighted case, the resulting
algorithm is $O(\log k/\log \log k)$-approximation. Also, we show that the
approximation factor can be in fact reduced to a constant for compatibility
graphs frequently occurring in practice.
  Finally, we show that the "empirical approximation factor" provided by the
above approach is very close to 1.

12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
2
The categories of this paper are: math
20
The categories of this paper are: acc-phys
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The categories of this paper are: atom-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-th