Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Position Heaps for Cartesian-tree Matching on Strings and Tries   The Cartesian-tree pattern matching is a recently introduced scheme of
pattern matching that detects fragments in a sequential data stream which have
a similar structure as a query pattern. Formally, Cartesian-tree pattern
matching seeks all substrings $S'$ of the text string $S$ such that the
Cartesian tree of $S'$ and that of a query pattern $P$ coincide. In this paper,
we present a new indexing structure for this problem called the Cartesian-tree
Position Heap (CPH). Let $n$ be the length of the input text string $S$, $m$
the length of a query pattern $P$, and $\sigma$ the alphabet size. We show that
the CPH of $S$, denoted $\mathsf{CPH}(S)$, supports pattern matching queries in
$O(m (\sigma + \log (\min\{h, m\})) + occ)$ time with $O(n)$ space, where $h$
is the height of the CPH and $occ$ is the number of pattern occurrences. We
show how to build $\mathsf{CPH}(S)$ in $O(n \log \sigma)$ time with $O(n)$
working space. Further, we extend the problem to the case where the text is a
labeled tree (i.e. a trie). Given a trie $T$ with $N$ nodes, we show that the
CPH of $T$, denoted $\mathsf{CPH}(T)$, supports pattern matching queries on the
trie in $O(m (\sigma^2 + \log (\min\{h, m\})) + occ)$ time with $O(N \sigma)$
space. We also show a construction algorithm for $\mathsf{CPH}(T)$ running in
$O(N \sigma)$ time and $O(N \sigma)$ working space.

13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
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The categories of this paper are: eess
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The categories of this paper are: q-fin
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The categories of this paper are: acc-phys
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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-ex
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The categories of this paper are: plasm-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: adap-org