熵有限文本的快速模式匹配

Shenfeng Chen, J. Reif
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引用次数: 2

摘要

我们提出了已知的第一个有界熵文本的一维和二维字符串匹配算法。设n为文本的长度,m为模式的长度。我们表明,对于模式分布的各种假设,算法的预期复杂性与文本的熵有关。对于均匀分布模式的情况,我们的一维匹配算法在O(nlogm/(pm))预期运行时间内工作,其中H是文本的熵,p=1-(1-H/sup 2/)/sup H/(1+H)/。如果V是生成模式的源的方差,则最坏情况下运行时间T也可以由(n log m/p(m+/spl radic/V))/spl les/T/spl les/(n log m/p(m-/spl radic/V))限定。我们的算法利用在某些无损数据压缩方案中发现的数据结构和概率分析技术。
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Fast pattern matching for entropy bounded text
We present the first known case of one-dimensional and two-dimensional string matching algorithms for text with bounded entropy. Let n be the length of the text and m be the length of the pattern. We show that the expected complexity of the algorithms is related to the entropy of the text for various assumptions of the distribution of the pattern. For the case of uniformly distributed patterns, our one dimensional matching algorithm works in O(nlogm/(pm)) expected running time where H is the entropy of the text and p=1-(1-H/sup 2/)/sup H/(1+H)/. The worst case running time T can also be bounded by (n log m/p(m+/spl radic/V))/spl les/T/spl les/(n log m/p(m-/spl radic/V)) if V is the variance of the source from which the pattern is generated. Our algorithm utilizes data structures and probabilistic analysis techniques that are found in certain lossless data compression schemes.
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