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Two strings of equal length are said to parameterized match if there is abijection that maps the characters of one string to those of the other string,so that two strings become identical. The parameterized pattern matchingproblem is, given two strings $T$ and $P$, to find the occurrences ofsubstrings in $T$ that parameterized match $P$. Diptarama et al. [PositionHeaps for Parameterized Strings, CPM 2017] proposed an indexing data structurecalled parameterized position heaps, and gave a left-to-right onlineconstruction algorithm. In this paper, we present a right-to-left onlineconstruction algorithm for parameterized position heaps. For a text string $T$of length $n$ over two kinds of alphabets $\Sigma$ and $\Pi$ of respective size$\sigma$ and $\pi$, our construction algorithm runs in $O(n \log(\sigma +\pi))$ time with $O(n)$ space. Our right-to-left parameterized position heapssupport pattern 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 occurrences to report. Our construction andpattern matching algorithms are as efficient as Diptarama et al.'s algorithms.

Right-to-left online construction of parameterized position heaps