Finding approximate palindromes in strings

We introduce a novel definition of approximate palindromes in strings, and provide an algorithm to find all maximal approximate palindromes in a string with up to $k$ errors. Our definition is based on the usual edit operations of approximate pattern matching, and the algorithm we give, for a string of size $n$ on a fixed alphabet, runs in $O(k^2 n)$ time. We also discuss two implementation-related improvements to the algorithm, and demonstrate their efficacy in practice by means of both experiments and an average-case analysis

Improved Algorithms for Approximate String Matching (Extended Abstract)

The problem of approximate string matching is important in many different areas such as computational biology, text processing and pattern recognition. A great effort has been made to design efficient algorithms addressing several variants of the problem, including comparison of two strings, approximate pattern identification in a string or calculation of the longest common subsequence that two strings share. We designed an output sensitive algorithm solving the edit distance problem between two strings of lengths n and m respectively in time O((s-|n-m|)min(m,n,s)+m+n) and linear space, where s is the edit distance between the two strings. This worst-case time bound sets the quadratic factor of the algorithm independent of the longest string length and improves existing theoretical bounds for this problem. The implementation of our algorithm excels also in practice, especially in cases where the two strings compared differ significantly in length. Source code of our algorithm is available at http://www.cs.miami.edu/\~dimitris/edit_distanceComment: 10 page

ZASTOSOWANIE ALGORYTMU WYSZUKIWANIA WIELU WZORCÓW OPARTEGO O TECHNIKĘ Q-GRAMÓW DO WYSZUKIWANIA PRZYBLIŻONEGO

We consider the application of multiple pattern matching (Multi AOSO on q-Grams) algorithm for approximate pattern matching. We propose the on-line approach which translates the problem from approximate pattern matching into a multiple pattern one (called partitioning into exact search). Presented solution allows relatively fast search multiple patterns in text with given k-differences(or mismatches). This paper presents comparison of solution based on MAG algorithm, and [4]. Experiments on DNA, English, Proteins and XML texts with up to k errors show that the new proposed algorithm achieves relatively good results in practical use.Rozważamy zastosowanie algorytmu wyszukiwania wielu wzorców (Multi AOSO on q-Grams) do wyszukiwania przybliżonego. Proponujemy rozwiązanie on-line, upraszczające problem wyszukiwania przybliżonego do wyszukiwania wielu wzorców. Zaprezentowane rozwiązanie umożliwia relatywnie szybko wyszukiwać wiele wzorców dla odległości Levenshteina (lub Hamminga) z ograniczeniem do k. W artykule porównane jest rozwiązanie oparte na algorytmie MAG oraz [4]. Badania eksperymentalne przeprowadzone na zbiorach DNA, English, Proteins and XML z różnymi wartościami k wykazały, że zaproponowany algorytm osiąga relatywnie dobre wyniki w praktycznym zastosowaniu

Application of Approximate Pattern Matching in Two Dimensional Spaces to Grid Layout for Biochemical Network Maps

Background For visualizing large-scale biochemical network maps, it is important to calculate the coordinates of molecular nodes quickly and to enhance the understanding or traceability of them. The grid layout is effective in drawing compact, orderly, balanced network maps with node label spaces, but existing grid layout algorithms often require a high computational cost because they have to consider complicated positional constraints through the entire optimization process. Results We propose a hybrid grid layout algorithm that consists of a non-grid, fast layout (preprocessor) algorithm and an approximate pattern matching algorithm that distributes the resultant preprocessed nodes on square grid points. To demonstrate the feasibility of the hybrid layout algorithm, it is characterized in terms of the calculation time, numbers of edge-edge and node-edge crossings, relative edge lengths, and F-measures. The proposed algorithm achieves outstanding performances compared with other existing grid layouts. Conclusions Use of an approximate pattern matching algorithm quickly redistributes the laid-out nodes by fast, non-grid algorithms on the square grid points, while preserving the topological relationships among the nodes. The proposed algorithm is a novel use of the pattern matching, thereby providing a breakthrough for grid layout. This application program can be freely downloaded from http://www.cadlive.jp/hybridlayout/hybridlayout.html