Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Optimal-Time Dictionary-Compressed Indexes   We describe the first self-indexes able to count and locate pattern
occurrences in optimal time within a space bounded by the size of the most
popular dictionary compressors. To achieve this result we combine several
recent findings, including \emph{string attractors} --- new combinatorial
objects encompassing most known compressibility measures for highly repetitive
texts ---, and grammars based on \emph{locally-consistent parsing}.
  More in detail, let $\gamma$ be the size of the smallest attractor for a text
$T$ of length $n$. The measure $\gamma$ is an (asymptotic) lower bound to the
size of dictionary compressors based on Lempel--Ziv, context-free grammars, and
many others. The smallest known text representations in terms of attractors use
space $O(\gamma\log(n/\gamma))$, and our lightest indexes work within the same
asymptotic space. Let $\epsilon>0$ be a suitably small constant fixed at
construction time, $m$ be the pattern length, and $occ$ be the number of its
text occurrences. Our index counts pattern occurrences in
$O(m+\log^{2+\epsilon}n)$ time, and locates them in $O(m+(occ+1)\log^\epsilon
n)$ time. These times already outperform those of most dictionary-compressed
indexes, while obtaining the least asymptotic space for any index searching
within $O((m+occ)\,\textrm{polylog}\,n)$ time. Further, by increasing the space
to $O(\gamma\log(n/\gamma)\log^\epsilon n)$, we reduce the locating time to the
optimal $O(m+occ)$, and within $O(\gamma\log(n/\gamma)\log n)$ space we can
also count in optimal $O(m)$ time. No dictionary-compressed index had obtained
this time before. All our indexes can be constructed in $O(n)$ space and
$O(n\log n)$ expected time.
  As a byproduct of independent interest...

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The categories of this paper are: nlin
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The categories of this paper are: q-bio
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The categories of this paper are: cmp-lg
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The categories of this paper are: econ
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The categories of this paper are: eess
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The categories of this paper are: cond-mat
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The categories of this paper are: comp-gas
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The categories of this paper are: physics
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The categories of this paper are: solv-int
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The categories of this paper are: dg-ga
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-alg
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The categories of this paper are: stat
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The categories of this paper are: adap-org