Efficient two-dimensional pattern matching in the presence of errors
TL;DR: The complexity of the algorithm for two-dimensional pattern matching in the presence of errors is O, where the pattern is an n 1 × n 2 array, the text is an m 1 × m 2 array and k is the number of mismatches allowed.
About: This article is published in Information Sciences.The article was published on 1987-12-01. It has received 42 citations till now. The article focuses on the topics: Pattern matching.
Citations
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27 May 2002TL;DR: This book presents a practical approach to string matching problems, focusing on the algorithms and implementations that perform best in practice, and includes all of the most significant new developments in complex pattern searching.
Abstract: This book presents a practical approach to string matching problems, focusing on the algorithms and implementations that perform best in practice. It covers searching for simple, multiple, and extended strings, as well as regular expressions, exactly and approximately. It includes all of the most significant new developments in complex pattern searching. The clear explanations, step-by-step examples, algorithms pseudo-code, and implementation efficiency maps will enable researchers, professionals, and students in bioinformatics, computer science, and software engineering to choose the most appropriate algorithms for their applications.
463 citations
01 Mar 1991
TL;DR: In this paper, the Smaller Matching Problem and the k-Aligned Ones with Location Problem are solved in O(kn2 √ m logm √ k log k + k 2n2) time.
Abstract: Finding all occurrences of a non-rectangular pattern of height m and area a in an n×n text with no more than k mismatch, insertion, and deletion errors is an important problem in computer vision. It can be solved using a dynamic programming approach in time O(an2). We show a O(kn2 √ m logm √ k log k + k2n2) algorithm which combines convolutions with dynamic programming. At the heart of the algorithm are the Smaller Matching Problem and the k-Aligned Ones with Location Problem. Efficient algorithms to solve both these problems are presented. The results presented in this paper appeared in the proceedings of the Second Symposium on Descrete Algorithms [AF91] College of Computing, Georgia Institute of Technology, Atlanta, GA 30332-0280; (404) 853-0083; amir@cc.gatech.edu; Partially supported by NSF grant IRI-9013055. DIMACS, Box 1179, Rutgers University, Piscataway, NJ 08855; (908) 932-5928; farach@dimacs.rutgers.edu
95 citations
TL;DR: The main contribution is a linear time algorithm for the problem of pattern matching with scaling, which is based on a new algorithmic approach to two-dimensional string matching and shows how to enhance it so that its running time may become sublinear with respect to the original redundant input representation.
92 citations
TL;DR: A serial algorithm for finding all appearances of the pattern in the text with a bounded total error in time O(2dnd log2 m) and an efficient solution to the close-match problem.
59 citations
TL;DR: A O(kn2 √ m logm √ k log k + k2n2) algorithm which combines convolutions with dynamic programming is shown which solves the Smaller Matching Problem and the k-Aligned Ones with Location Problem.
Abstract: Efficient algorithms exist for the approximate two dimensional matching problem for rectangles. This is the problem of finding all occurrences of an m × m pattern in an n × n text with no more than k mismatch, insertion, and deletion errors. In computer vision it is important to generalize this problem to non-rectangular figures. We make progress towards this goal by defining half-rectangular figures of height m and area a. The approximate two dimensional matching problem for half-rectangular patterns can be solved using a dynamic programming approach in time O(an2). We show an O(kn2formula]formula] + k2n2) algorithm which combines convolutions with dynamic programming. Note that our algorithm is superior to previous known solutions for k ? m13. At the heart of the algorithm are the Smaller Matching Problem and the k-Aligned Ones with Location Problem. These are interesting problems in their own right. Efficient algorithms to solve both these problems are presented.
58 citations
References
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18 Feb 2018TL;DR: An algorithm for finding all occurrences of the pattern in the text, each with at most k mismatches, runs in O( k ( m log m + n )) time.
Abstract: Given a text of length n , a pattern of length m , and an integer k , we present an algorithm for finding all occurrences of the pattern in the text, each with at most k mismatches. The algorithm runs in O( k ( m log m + n )) time.
201 citations
TL;DR: The purpose is to give an algorithm for thz! two dimensional case, one which follows the general approach of the K MP, and indeed uses the KMP as a subprogram, which has a running time of 0(n2 + m’), which is clearly optimal since both the pattern and the text have to be read and this takes O(rt’ + m2).
143 citations
"Efficient two-dimensional pattern m..." refers methods in this paper
...The algorithm uses a partition of the set of m - 1 rows into log m sets as follows: [1],[2,3],....
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01 Nov 1986
TL;DR: Given a text of length n, a pattern of length m and an integer k, this paper presents parallel and serial algorithms for finding all occurrences of the pattern in the text with at most k differences.
Abstract: Consider the stnng matching problem, where differences between characters of the pattern and characters of the text are allowed. Each difference is due to either a mismatch between a character of the text and a character of the pattern or a superfluous character in the text or a superfluous character in the pattern. Given a text of length n, a pattern of length m and an integer k, we present parallel and serial algorithms for finding all occurrences of the pattern in the text with at most k differences. The first part of the parallel algorithm consists of analysis of the pattern and takes 0 (log m ) time using m 2 processors. The rest of the algorithm consists of handling the text. The text han1. The research of this author was supported by NSF grants NSF-DCR-8318874 and NSF-DCR-8413359 and ONR grant
136 citations
21 Oct 1985
TL;DR: An algorithm for finding all occurrences of the pattern in the text, each with at most k mismatches (superfluous characters in either the text or the pattern are not allowed), which runs in O(k(m logm + n)) time.
Abstract: Consider the string matching problem where differences between characters of the pattern and characters of the text are allowed. Each difference is due to either a mismatch between a character of the text and a character of the pattern or a superfluous character in the text or a superfluous character in the pattern. Given a text of length n, a pattern of length m and an integer k, we present an algorithm for finding all occurrences of the pattern in the text, each with at most k differences. The algorithm runs in O(m2 + k2n) time. Given the same input we also present an algorithm for finding all occurrences of the pattern in the text, each with at most k mismatches (superfluous characters in either the text or the pattern are not allowed). This algorithm runs in O(k(m logm + n)) time.
78 citations