在线性平均时间内（大多数情况下）使用反转和易位的字符串匹配
String Matching with Inversions and Translocations in Linear Average Time (Most of the Time)
摘要：
我们提出了一个有效的算法，找到一个给定的模式$p$的长度$m$的所有近似出现在一个文本$t$的长度$n$允许易位等长度相邻的因素和反转的因素。该算法基于一种有效的过滤方法，在最坏情况下具有$\bigO(nm\max(α, β))$ -时间复杂度和$\bigO(\max(α, β))$ -空间复杂度，其中$α$和$β$分别是涉及任意移位和反转的因子的最大长度.此外，我们表明，在等概率和字符的独立性的假设下，我们的算法有一个$\bigO(n)$平均时间复杂度，每当$σ= Ω(\log m / \log\log^{1-ε} m)$，其中$ε> 0$和$σ$是字母表的维数。实验表明，该算法在实际应用中取得了很好的效果.
英文摘要：
We present an efficient algorithm for finding all approximate occurrences of a given pattern $p$ of length $m$ in a text $t$ of length $n$ allowing for translocations of equal length adjacent factors and inversions of factors. The algorithm is based on an efficient filtering method and has an $\bigO(nm\max(α, β))$-time complexity in the worst case and $\bigO(\max(α, β))$-space complexity, where $α$ and $β$ are respectively the maximum length of the factors involved in any translocation and inversion. Moreover we show that under the assumptions of equiprobability and independence of characters our algorithm has a $\bigO(n)$ average time complexity, whenever $σ= Ω(\log m / \log\log^{1-ε} m)$, where $ε> 0$ and $σ$ is the dimension of the alphabet. Experiments show that the new proposed algorithm achieves very good results in practical cases.
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