Let $\mathcal{P}$ be a collection of d patterns $\{{\mathsf{P}}_1,{\mathsf{P}}_2,\dots ,{\mathsf{P}}_d\}$ of total length n characters, which are chosen from an alphabet Σ of size σ. Given a text T (over Σ), the dictionary indexing problem is to create a data structure using which we can report all positions j (called occurrences) where at least one of the patterns ${\mathsf{P}}_i\in \mathcal{P}$ is a match with the same-length substring of T that starts at j. We consider this problem under the following definitions of matching.

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Parameterized Matching: The characters of Σ are partitioned into static characters and parameterized characters. Two equal length strings S and $S^{\prime }$ are a parameterized match iff the static characters match exactly, and there exists a one-to-one function which renames the parameterized characters in S to those in $S^{\prime }$.

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Order-Preserving Matching: The alphabet Σ is ordered. Two equal length strings S and $S^{\prime }$ are an order-preserving match iff for any two integers $i,j\in [1,|S|]$, $S[i]\prec S[j]\iff S^{\prime }[i]\prec S^{\prime }[j]$, where ≺ denotes the precedence order in Σ.

让 $\mathcal{P}$是d模式的集合$\{{\mathsf{P}}_{\mathrm{1个}}，{\mathsf{P}}_2，\dots ，{\mathsf{P}}_d\}$总长度为n个字符的字符，可从大小为σ的字母Σ中选择。给定文本T（超过Σ），字典索引问题是创建一个数据结构，通过该数据结构，我们可以报告所有位置j（称为出现）的位置，其中至少有一种模式${\mathsf{P}}_{\mathrm{一世}}\in \mathcal{P}$是与以j开头的T的相同长度子字符串匹配的项。我们在以下匹配定义下考虑此问题。

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参数化匹配： Σ的字符分为静态字符和参数化字符。两个相等长度的字符串S和${\mathrm{小号}}^{\prime }$是一个参数化匹配当且仅当静态字符完全匹配，并且存在一个一到一个功能，其将重命名参数化的字符小号的那些${\mathrm{小号}}^{\prime }$。

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保留顺序匹配：字母Σ已排序。两个相等长度的字符串S和${\mathrm{小号}}^{\prime }$ 是任何两个整数的保留顺序匹配iff $\mathrm{一世}，Ĵ\in [\mathrm{1个}，|\mathrm{小号}|]$， $\mathrm{小号}[\mathrm{一世}]\prec \mathrm{小号}[Ĵ]\iff {\mathrm{小号}}^{\prime }[\mathrm{一世}]\prec {\mathrm{小号}}^{\prime }[Ĵ]$，其中≺表示Σ中的优先顺序。