Approximate string matching

About: Approximate string matching is a research topic. Over the lifetime, 1903 publications have been published within this topic receiving 62352 citations. The topic is also known as: fuzzy string-searching algorithm & fuzzy string-matching algorithm.

Efficient comparison based string matching

Abstract: We study the exact number of symbol comparisons that are required to solve the string matching problem and present a family of efficient algorithms. Unlike previous string matching algorithms, the algorithms in this family do not "forget" results of comparisons, what makes their analysis much simpler. In particular, we give a linear-time algorithm that finds all occurrences of a pattern of length m in a text of length n in [formula] comparisons. The pattern preprocessing takes linear time and makes at most 2 m comparisons. This algorithm establishes that, in general, searching for a long pattern is easier than searching for a short one. We also show that any algorithm in the family of the algorithms presented must make at least [formula] symbol comparisons, for m = 2 k − 1 and any integer k ≥ 1.

Approximate Cover of Strings.

Abstract: Regularities in strings arise in various areas of science, including coding and automata theory, formal language theory, combinatorics, molecular biology and many others. A common notion to describe regularity in a string T is a cover, which is a string C for which every letter of T lies within some occurrence of C. The alignment of the cover repetitions in the given text is called a tiling. In many applications finding exact repetitions is not sufficient, due to the presence of errors. In this paper, we use a new approach for handling errors in coverable phenomena and define the approximate cover problem (ACP), in which we are given a text that is a sequence of some cover repetitions with possible mismatch errors, and we seek a string that covers the text with the minimum number of errors. We first show that the ACP is NP -hard, by studying the cover-length relaxation of the ACP, in which the requested length of the approximate cover is also given with the input string. We show that this relaxation is already NP -hard. We also study another two relaxations of the ACP, which we call the partial-tiling relaxation of the ACP and the full-tiling relaxation of the ACP, in which a tiling of the requested cover is also given with the input string. A given full tiling retains all the occurrences of the cover before the errors, while in a partial tiling there can be additional occurrences of the cover that are not marked by the tiling. We show that the partial-tiling relaxation has a polynomial time complexity and give experimental evidence that the full-tiling also has polynomial time complexity. The study of these relaxations, besides shedding another light on the complexity of the ACP, also involves a deep understanding of the properties of covers, yielding some key lemmas and observations that may be helpful for a future study of regularities in the presence of errors.

Method of determining the similarity of two strings

Abstract: Embodiments of the present invention provide a method of determining the similarity of two strings. The method comprises calculating a Levenshtein matrix of a first string and a second string. A Levenshtein distance is determined from the Levenshtein matrix. A largest common substring is also determined from the Levenshtein matrix. The method may farther comprise determining a numerical score as a function of the Levenshtein distance and the largest common substring.