Shift-or string matching with super-alphabets

Given a text T[1…n] and a pattern P[1…m] over some alphabet Σ of size σ, we want to find all the (exact) occurrences of P in T. The well-known shift-or algorithm solves this problem in time O(n⌈m/w⌉), where w is the number of bits in machine word, using bit-parallelism. We show how to extend the bit-parallelism in another direction, using super-alphabets. This gives a speed-up by a factor s, where s is the number of characters processed simultaneously. The algorithm is implemented, and we show that it works well in practice too. The result is the fastest known algorithm for exact string matching for short patterns and small alphabets.     

Approximate string matching with suffix automata

Theapproximate string matching problem is, given a text string, a pattern string, and an integerk, to find in the text all approximate occurrences of the pattern. An approximate occurrence means a substring of the text with edit distance at mostk from the pattern. We give a newO(kn) algorithm for this problem, wheren is the length of the text. The algorithm is based on the suffix automaton with failure transitions and on the diagonalwise monotonicity of the edit distance table. Some experiments showing that the algorithm has a small overhead are reported.     

Improving practical exact string matching

We present improved variations of the BNDM algorithm for exact string matching. At each alignment our bit-parallel algorithms process a q-gram before testing the state variable. In addition we apply reading a 2-gram in one instruction. Our point of view is practical efficiency of algorithms. Our experiments show that the new variations are faster than earlier algorithms in many cases.     

Scaled and permuted string matching

The goal of scaled permuted string matching is to find all occurrences of a pattern in a text, in all possible scales and permutations. Given a text of length n and a pattern of length m we present an O(n) algorithm.     

On building minimal automaton for subset matching queries

We address the problem of building an index for a set D of n strings, where each string location is a subset of some finite integer alphabet of size σ, so that we can answer efficiently if a given simple query string (where each string location is a single symbol) p occurs in the set. That is, we need to efficiently find a string d∈D such that p[i]∈d[i] for every i. We show how to build such index in O(nlogσ/Δ(σ)log(n)) average time, where Δ is the average size of the subsets. Our methods have applications e.g. in computational biology (haplotype inference) and music information retrieval.     

Improving the bit-parallel NFA of Baeza-Yates and Navarro for approximate string matching

We propose a new variant of the bit-parallel NFA of Baeza-Yates and Navarro (BPD) for approximate string matching [R. Baeza-Yates, G. Navarro, Faster approximate string matching, Algorithmica 23 (1999) 127-158]. BPD is one of the most practical approximate string matching algorithms under moderate pattern lengths and error levels [G. Myers, A fast bit-vector algorithm for approximate string matching based on dynamic programming, J. ACM 46 (3) 1989 395-415; G. Navarro, M. Raffinot, Flexible Pattern Matching in Strings—Practical On-line Search Algorithms for Texts and Biological Sequences, Cambridge University Press, Cambridge, UK, 2002]. Given a length-m pattern and an error threshold k, the original BPD requires (m−k)(k+2) bits of space to represent an NFA with (m−k)(k+1) states. In this paper we remove redundancy from the original NFA representation. Our variant requires (m−k)(k+1) bits of space, which is optimal in the sense that exactly one bit per state is used. The space efficiency is achieved by using an alternative, but equally or even more efficient, simulation algorithm for the bit-parallel NFA. We also present experimental results to compare our modified NFA against the original BPD and its main competitors. Our new variant is more efficient than the original BPD, and it hence takes over/extends the role of the original BPD as one of the most practical approximate string matching algorithms under moderate values of k and m.     

一种适用于大规模特征集的快速匹配算法

提出了一种适用于大规模特征集的快速匹配算法——SRS算法,该算法性能优异,在特征集达到100 000条时,匹配速度比经典算法快10倍以上。该算法适用于内容过滤、防病毒、反垃圾邮件、短信过滤、网络入侵检测和防御等众多领域。     

Giant complete automaton for uncertain multiple string matching and its high speed construction algorithm

Multiple string matching is often completed under the presence of U- or V-uncertain-strings,or combinations thereof.Recognizing large numbers of strings with U-, V-,and U-V-uncertain-strings,including the interleaving of two or more uncertain strings,is important to thoroughly gathering useful information and detecting harmful information.This paper proposes a complete automaton and its high-speed construction algorithm for large-scale U-, V-,and U-V-uncertain multiple strings,including two or more uncertai...     

巨型多不确定串匹配完全自动机及其快速生成算法

在串匹配搜索中,字符串常常采用U-不确定串、V-不确定串及其结合的U-V-不确定串.如何识别巨量U-不确定字符串、V-不确定字符串和U-V-不确定字符串,以及两个和两个以上U-V-不确定字符串的交错情况的串匹配,是没有遗漏地检测有害信息的关键问题.本文提出一个快速检测巨量U-不确定字符串、巨量V-不确定字符串和巨量U-V-不确定字符串的多串匹配完全自动机及其快速生成方法,包括两个和两个以上不确定字符串相互交错的情况;并且给出V-不确定字符串的完全自动机的最大并行台数,指出通常正则表达式匹配可能出现相似连接和交错情况的两种遗漏,指出如果没有从整体的角度对U-不确定串中的字符子串集进行两两不相交化及无同源后续奇点化的处理,结果就可能出现错误或者增加状态数目.     

Finding rotational symmetries by cyclic string matching

Symmetry is an important shape feature. In this paper, a simple and fast method to detect perfect and distorted rotational symmetries of 2D objects is described. The boundary of a shape is polygonally approximated and represented as a string. Rotational symmetries are found by cyclic string matching between two identical copies of the shape string. The set of minimum cost edit sequences that transform the shape string to a cyclically shifted version of itself define the rotational symmetry and its order. Finally, a modification of the algorithm is proposed to detect reflectional symmetries. Some experimental results are presented to show the reliability of the proposed algorithm.     

一种改进的BM字符串匹配算法

经典字符串匹配算法的本质都是从左向右或者从右向左顺序进行字符匹配的,在主串中存在大量子串与模式串前缀或者后缀相同时效率较低,并且模式串最大右移长度为模式串长度。改进算法采用二分匹配字符串的方法,有效地避免了由主串中大量子串与模式串前缀相同或者后缀相同引起的无意义比较次数。模式串的移动距离根据改进的坏字符规则进行计算,增大了模式串的移动距离。实验结果表明,改进的字符串匹配算法可以有效地减少字符串的匹配次数和移动次数,达到了提高算法效率的目的。     

Experiments on string matching in memory structures

Various string matching algorithms have been designed and some experimental work on string matching over bounded alphabets has been performed, but string matching over unbounded alphabets has been little investigated. We present here experimental results where symbols are taken among potentially infinite sets such as integers, reals or composed structures. These results show that, in most cases, it is better to decompose each symbol into a sequence of bytes and use algorithms which assume that the alphabet is bounded, and use heuristics on symbols. © 1998 John Wiley & Sons, Ltd.     

Parameterized matching on non-linear structures

The classical pattern matching paradigm is that of seeking occurrences of one string in another, where both strings are drawn from an alphabet set Σ. In the parameterized pattern matching model, a consistent renaming of symbols from Σ is allowed in a match. The parameterized matching paradigm has proven useful in problems in software engineering, computer vision, and other applications. In classical pattern matching, both the text and pattern are strings. Applications such as searching in xml or searching in hypertext require searching strings in non-linear structures such as trees or graphs. There has been work in the literature on exact and approximate parameterized matching, as well as work on exact and approximate string matching on non-linear structures. In this paper we explore parameterized matching in non-linear structures. We prove that exact parameterized matching on trees can be computed in linear time for alphabets in an O(n)-size integer range, and in time O(nlogm) in general, where n is the tree size and m the pattern length. These bounds are optimal in the comparison model. We also show that exact parameterized matching on directed acyclic graphs (DAGs) is NP-complete.     

改进的多模式字符串匹配算法

在经典的AC多模式字符串匹配算法的基础上,结合BMH算法的优点,提出了一种快速的多模式字符串匹配算法。一般情况下,该算法不需要匹配目标文本串中的每个字符,而是在实际比较之前跳过尽可能多的字符,以减少字符比较的操作,实现快速匹配。在模式串较长和较短的情况下,算法都有很好的性能。实验表明,在模式串较短时,本算法所需的时间仅为AC算法的50%～30%;在模式串较长时,所需时间为AC算法的26.7%～15.2%。     

An aggressive algorithm for multiple string matching

A new algorithm based on the Wu-Manber algorithm for multiple string matching is presented in this paper. The algorithm eliminates the functional overlap of the table HASH and SHIFT, and computes the shift distances in an aggressive manner. After each test, the algorithm examines the character next to the scan window to maximize the shift distance. This idea is consistent with that of the quick-search (QS) algorithm. Experimental results on four alphabets show that the new algorithm is more efficient than Wu-Manber and other recent algorithms, particularly on short pattern sets and large alphabet.     

BM串匹配的一个改进算法

在分析BM算法和文献[12]的基础上,给出了BM串匹配的一个改进算法。该算法有以下重要的特点：1)最坏情况下,算法有效地减少了字符重复比较的次数,提高了匹配效率;2)匹配算法在二维匹配和不精确匹配中较易推广。     

Approximate string matching using withinword parallelism

Given a text string, a pattern string, and an integer k, the problem of approximate string matching with k differences is to find all substrings of the text string whose edit distance from the pattern string is less than k. The edit distance between two strings is defined as the minimum number of differences, where a difference can be a substitution, insertion, or deletion of a single character. An implementation of the dynamic programming algorithm for this problem is given that packs several characters and mod-4 integers into a computer word. Thus, it is a parallelization of the conventional implementation that runs on ordinary processors. Since a small alphabet means that characters have short binary codes, the degree of parallelism is greatest for small alphabets and for processors with long words. For an alphabet of size 8 or smaller and a 64 bit processor, a 21-fold parallelism over the conventional algorithm can be obtained. Empirical comparisons to the basic dynamic programming algorithm, to a version of Ukkonen's algorithm, to the algorithm of Galil and Park, and to a limited implementation of the Wu-Manber algorithm are given.     

Boyer-Moore串匹配算法的改进

在分析Boyer-Moore (BM)算法的基础上,提出了BM算法的一个新的变形。其基本思想是在算法的预处理阶段,对扩展模式串Pa建立好后缀规则,其中：P是模式串,a是字母表中的任一字符,既加大了已匹配后缀的长度,同时隐含了Sunday算法的坏字符规则,从而获得更大的窗口跳跃距离。理论分析证明,该算法具有线性最差时间复杂度和亚线性平均时间复杂度,空间复杂度为O(m(σ+1))。实验结果表明,该算法的实际性能与BM算法相比有明显改善,尤其适合小字母表的情形。