Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Optimal Encodings for Range Top-k, Selection, and Min-Max   We consider encoding problems for range queries on arrays. In these problems
the goal is to store a structure capable of recovering the answer to all
queries that occupies the information theoretic minimum space possible, to
within lower order terms. As input, we are given an array $A[1..n]$, and a
fixed parameter $k \in [1,n]$. A range top-$k$ query on an arbitrary range
$[i,j] \subseteq [1,n]$ asks us to return the ordered set of indices $\{\ell_1,
..., \ell_{k}\}$ such that $A[\ell_m]$ is the $m$-th largest element in
$A[i..j]$, for $1 \le m \le k$. A range selection query for an arbitrary range
$[i,j] \subseteq [1,n]$ and query parameter $k' \in [1,k]$ asks us to return
the index of the $k'$-th largest element in $A[i..j]$. We completely resolve
the space complexity of both of these heavily studied problems---to within
lower order terms---for all $k = o(n)$. Previously, the constant factor in the
space complexity was known only for $k=1$. We also resolve the space complexity
of another problem, that we call range min-max, in which the goal is to return
the indices of both the minimum and maximum elements in a range.

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The categories of this paper are: nucl-th
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The categories of this paper are: adap-org
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The categories of this paper are: funct-an
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The categories of this paper are: hep-th
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The categories of this paper are: econ
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
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The categories of this paper are: stat
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The categories of this paper are: chem-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-ex
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The categories of this paper are: math
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The categories of this paper are: eess