Journal ArticleDOI
On the Worst-Case Behavior of String-Searching Algorithms
TLDR
There do not exist pattern matching algorithms whose worst-case behavior is “sublinear” in n (that is, linear with constant less than one), in contrast with the situation for average behavior (the Boyer-Moore algorithm is known to be sublinear on the average).Abstract:
Any algorithm for finding a pattern of length k in a string of length n must examine at least $n - k + 1$ of the characters of the string in the worst case. By considering the pattern $00 \cdots 0$, we prove that this is the best possible result. Therefore there do not exist pattern matching algorithms whose worst-case behavior is “sublinear” in n (that is, linear with constant less than one), in contrast with the situation for average behavior (the Boyer-Moore algorithm is known to be sublinear on the average).read more
Citations
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Information Retrieval: Data Structures and Algorithms
TL;DR: For programmers and students interested in parsing text, automated indexing, its the first collection in book form of the basic data structures and algorithms that are critical to the storage and retrieval of documents.
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Journal ArticleDOI
String overlaps, pattern matching, and nontransitive games
TL;DR: The key notion of the correlation of two strings is introduced, which is a representation of how the second string can overlap into the first, and this notion is used to state and prove a formula for the generating function that enumerates the q -ary strings of length n which contain none of a given finite set of patterns.
Book ChapterDOI
Algorithms for finding patterns in strings
TL;DR: This chapter discusses the algorithms for solving string-matching problems that have proven useful for text-editing and text-processing applications and several innovative, theoretically interesting algorithms have been devised that run significantly faster than the obvious brute-force method.
Journal ArticleDOI
Two-way string-matching
TL;DR: A new string-matching algorithm is presented, which can be viewed as an intermediate between the classical algorithms of Knuth, Morris, and Pratt and Boyer and Moore, which presents the advantage of being remarkably simple which consequently makes its analysis possible.
References
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Journal ArticleDOI
Fast Pattern Matching in Strings
TL;DR: An algorithm is presented which finds all occurrences of one given string within another, in running time proportional to the sum of the lengths of the strings, showing that the set of concatenations of even palindromes, i.e., the language $\{\alpha \alpha ^R\}^*$, can be recognized in linear time.
Journal ArticleDOI
A fast string searching algorithm
TL;DR: The algorithm has the unusual property that, in most cases, not all of the first i.” in another string, are inspected.
Proceedings ArticleDOI
A generalization and proof of the Aanderaa-Rosenberg conjecture
Ronald L. Rivest,Jean Vuillemin +1 more
TL;DR: A non-constructive argument (not based on the construction of an “oracle”) proves the generalized conjecture for d a prime power, showing that at least v2/9 entries of the adjacency matrix of a v-vertex undirected graph G must be examined in the worst case to determine if G has any given non-trivial monotone graph property.