Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fast Algorithms for the Shortest Unique Palindromic Substring Problem on
  Run-Length Encoded Strings   For a string $S$, a palindromic substring $S[i..j]$ is said to be a
\emph{shortest unique palindromic substring} ($\mathit{SUPS}$) for an interval
$[s, t]$ in $S$, if $S[i..j]$ occurs exactly once in $S$, the interval $[i, j]$
contains $[s, t]$, and every palindromic substring containing $[s, t]$ which is
shorter than $S[i..j]$ occurs at least twice in $S$. In this paper, we study
the problem of answering $\mathit{SUPS}$ queries on run-length encoded strings.
We show how to preprocess a given run-length encoded string $\mathit{RLE}_{S}$
of size $m$ in $O(m)$ space and $O(m \log \sigma_{\mathit{RLE}_{S}} + m
\sqrt{\log m / \log\log m})$ time so that all $\mathit{SUPSs}$ for any
subsequent query interval can be answered in $O(\sqrt{\log m / \log\log m} +
\alpha)$ time, where $\alpha$ is the number of outputs, and
$\sigma_{\mathit{RLE}_{S}}$ is the number of distinct runs of
$\mathit{RLE}_{S}$. Additionaly, we consider a variant of the SUPS problem
where a query interval is also given in a run-length encoded form. For this
variant of the problem, we present two alternative algorithms with faster
queries. The first one answers queries in $O(\sqrt{\log\log m /\log\log\log m}
+ \alpha)$ time and can be built in $O(m \log \sigma_{\mathit{RLE}_{S}} + m
\sqrt{\log m / \log\log m})$ time, and the second one answers queries in
$O(\log \log m + \alpha)$ time and can be built in $O(m \log
\sigma_{\mathit{RLE}_{S}})$ time. Both of these data structures require $O(m)$
space.

22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
5
The categories of this paper are: gr-qc
28
The categories of this paper are: alg-geom
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics