The.Algorithm.Design.Manual.Springer-Verlag.1998
Share Embed Flag
Download ePaper

The.Algorithm.Design.Manual.Springer-Verlag.1998

The.Algorithm.Design.Manual.Springer-Verlag.1998 The.Algorithm.Design.Manual.Springer-Verlag.1998

omarfabiano
18.04.2013 Views

String Matching Next: Approximate String Matching Up: Set and String Problems Previous: Set Packing String Matching Input description: A text string t of length n. A pattern string p of length m. Problem description: Find the first (or all) instances of the pattern in the text. Discussion: String matching is fundamental to database and text processing applications. Every text editor must contain a mechanism to search the current document for arbitrary strings. Pattern matching programming languages such as Perl and Awk derive much of their power from their built-in string matching primitives, making it easy to fashion programs that filter and modify text. Spelling checkers scan an input text for words in the dictionary and reject any strings that do not match. Several issues arise in identifying the right string matching algorithm for the job: ● Are your search patterns and/or texts short? - If your strings are sufficiently short and your queries sufficiently infrequent, the brute-force O(m n)-time search algorithm will likely suffice. For each possible starting position , it tests whether the m characters starting from the ith position of the text are identical to the pattern. For very short patterns, say , you can't hope to beat brute force by much, if at all, and you file:///E|/BOOK/BOOK5/NODE203.HTM (1 of 4) [19/1/2003 1:32:08]

String Matching shouldn't try. Further, since we can reject the possibility of a match at a given starting position the instant we observe a text/pattern mismatch, we expect much better than O(mn) behavior for typical strings. Indeed, the trivial algorithm usually runs in linear time. But the worst case certainly can occur, as with pattern and text . ● What about longer texts and patterns? - By being more clever, string matching can be performed in worst-case linear time. Observe that we need not begin the search from scratch on finding a character mismatch between the pattern and text. We know something about the subsequent characters of the string as a result of the partial match from the previous position. Given a long partial match from position i, we can jump ahead to the first character position in the pattern/text that will provide new information about the text starting from position i+1. The Knuth-Moris- Pratt algorithm preprocesses the search pattern to construct such a jump table efficiently. The details are tricky to get correct, but the resulting implementations yield short, simple programs. Even better in practice is the Boyer-Moore algorithm, although it offers similar worst-case performance. Boyer-Moore matches the pattern against the text from right to left, in order to avoid looking at large chunks of text on a mismatch. Suppose the pattern is abracadabra, and the eleventh character of the text is x. This pattern cannot match in any of the first eleven starting positions of the text, and so the next necessary position to test is the 22nd character. If we get very lucky, only n/m characters need ever be tested. The Boyer-Moore algorithm involves two sets of jump tables in the case of a mismatch: one based on pattern matched so far, the other on the text character seen in the mismatch. Although somewhat more complicated than Knuth-Morris-Pratt, it is worth it in practice for patterns of length m > 5. ● Will you perform multiple queries on the same text? - Suppose you were building a program to repeatedly search a particular text database, such as the Bible. Since the text remains fixed, it pays build a data structure to speed up search queries. The suffix tree and suffix array data structures, discussed in Section , are the right tools for the job. ● Will you search many texts using the same patterns? - Suppose you were building a program to screen out dirty words from a text stream. Here, the set of patterns remains stable, while the search texts are free to change. In such applications, we may need to find all occurrences of each of k different patterns, where k can be quite large. Performing a linear-time search for each of these patterns yields an O(k (m+n)) algorithm. If k is large, a better solution builds a single finite automaton that recognizes each of these patterns and returns to the appropriate start state on any character mismatch. The Aho-Corasick algorithm builds such an automaton in linear time. Space savings can be achieved by optimizing the pattern recognition automaton, as discussed in Section . This algorithm was used in the original version of fgrep. Sometimes multiple patterns are specified not as a list of strings, but concisely as a regular expression. For example, the regular expression matches any string on (a,b,c) that begins and ends with an a, including a itself. The best way to test whether input strings are described by a given regular expression R is to construct the finite automaton equivalent to R and file:///E|/BOOK/BOOK5/NODE203.HTM (2 of 4) [19/1/2003 1:32:08]

String Matching<br />

Next: Approximate String Matching Up: Set and String Problems Previous: Set Packing<br />

String Matching<br />

Input description: A text string t of length n. A pattern string p of length m.<br />

Problem description: Find the first (or all) instances of the pattern in the text.<br />

Discussion: String matching is fundamental to database and text processing applications. Every text<br />

editor must contain a mechanism to search the current document for arbitrary strings. Pattern matching<br />

programming languages such as Perl and Awk derive much of their power from their built-in string<br />

matching primitives, making it easy to fashion programs that filter and modify text. Spelling checkers<br />

scan an input text for words in the dictionary and reject any strings that do not match.<br />

Several issues arise in identifying the right string matching algorithm for the job:<br />

● Are your search patterns and/or texts short? - If your strings are sufficiently short and your<br />

queries sufficiently infrequent, the brute-force O(m n)-time search algorithm will likely suffice.<br />

For each possible starting position , it tests whether the m characters starting<br />

from the ith position of the text are identical to the pattern.<br />

For very short patterns, say , you can't hope to beat brute force by much, if at all, and you<br />

file:///E|/BOOK/BOOK5/NODE203.HTM (1 of 4) [19/1/2003 1:32:08]

logo

products

Resources

Company

Terms of service
Privacy policy
Cookie policy
Cookie settings
Imprint
Change language
Made with love in Switzerland
© 2024 Yumpu.com all rights reserved

Hooray! Your file is uploaded and ready to be published.

Saved successfully!

Ooh no, something went wrong!