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arXiv · 1903.06289

The Parameterized Position Heap of a Trie

Noriki Fujisato·Yuto Nakashima·Shunsuke Inenaga·Hideo Bannai·Masayuki Takeda
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Abstract

Let $\Sigma$ and $\Pi$ be disjoint alphabets of respective size $\sigma$ and $\pi$. Two strings over $\Sigma \cup \Pi$ of equal length are said to parameterized match (p-match) if there is a bijection $f:\Sigma \cup \Pi \rightarrow \Sigma \cup \Pi$ such that (1) $f$ is identity on $\Sigma$ and (2) $f$ maps the characters of one string to those of the other string so that the two strings become identical. We consider the p-matching problem on a (reversed) trie $\mathcal{T}$ and a string pattern $P$ such that every path that p-matches $P$ has to be reported. Let $N$ be the size of the given trie $\mathcal{T}$. In this paper, we propose the parameterized position heap for $\mathcal{T}$ that occupies $O(N)$ space and supports p-matching queries in $O(m \log (\sigma + \pi) + m \pi + \mathit{pocc}))$ time, where $m$ is the length of a query pattern $P$ and $\mathit{pocc}$ is the number of paths in $\mathcal{T}$ to report. We also present an algorithm which constructs the parameterized position heap for a given trie $\mathcal{T}$ in $O(N (\sigma + \pi))$ time and working space.

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Noriki Fujisato, Yuto Nakashima, Shunsuke Inenaga, Hideo Bannai, Masayuki Takeda. 2019-03-14. The Parameterized Position Heap of a Trie. https://arxiv.org/abs/1903.06289

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