Computing Patterns in Strings
Francine Blanchet-Sadri
University of North Carolina
P.O. Box 26170
Greensboro, NC 27402-6170

Contact Information
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Phone: (336) 256-1125, Fax: (336) 256-0439

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List of Supported Students

Project Award Information

Strings, Patterns, Periods, Repetitions, Covers, Seeds, Approximate Patterns, Distance Measures, String Algorithms, Dynamic Programming. 

Project Summary

The problem of computing patterns in sequences or strings of characters from a finite alphabet has important applications in numerous areas of computer science, notably in data compression, information theory, and pattern matching. This problem has also important applications in biology. The stimulus for such recent works is the study of biological sequences such as DNA and protein that play a central role in molecular biology. DNA sequences can be viewed as quite long but finite strings of nucleotides of 4 different types, while protein sequences can be viewed as finite strings of amino acids of 20 possible types. Patterns such as periodicities and repetitions make up a significant fraction of both DNA and protein sequences. Although the functions of these patterns are not well understood, they appear important for understanding the expression, regulation and evolution of a biological sequence. These patterns can be used to identify the sequence among other sequences, an application that plays a role in genetic fingerprinting. Repetitions in biological sequences have been associated with human genetic diseases. They also complicate multiple sequence alignment because matches may be present in numerous places.

        The literature has generally considered problems in which a period u of a repetition is invariant. It has been required that occurrences of u match each other exactly. Due to the action of evolutionary mutation, patterns in biological strings are seldom exact but rather approximate. It therefore becomes necessary to recognize u' as an occurence of u if the distance between u' and u is bounded by a certain threshold. Several definitions of distance have been proposed like the Hamming distance which counts the minimum number of character substitutions required to transform u' into u, and the edit distance which counts the minimum number of substitutions, insertions, and deletions of characters required to transform u' into u. Although there is an enormous literature dealing with approximate pattern matching according to these and other definitions of distance, very little is known on approximate repetitions, a version of repetitions where errors are allowed, and much remains to be done.

        Given the importance of patterns in biological strings and the exponential growth in the size of the DNA database, it is important to develop efficient methods for detecting these patterns. This project studies patterns such as periodicities, repetitions, covers, and seeds and their approximate versions built upon various commonly used distance measures. It is natural to consider approximate string matching techniques when developing algorithms for approximate patterns. Techniques that might prove useful include recent combinatorial techniques related to partial strings which are strings where a number of gap characters are allowed. Techniques also include the cover array, the highest scoring paths in weighted grid graphs, the probabilistic models that have been proposed for repetitions, and the subtree max gap problem which seems to be a powerful tool in parallel algorithm design. Several students, undergraduate and graduate, were involved in different aspects of this project.

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Project Impact
The following students have been involved in various stages of this project:
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NSF home page. Acknowledgement: This material is based upon work supported by the National Science Foundation under grant No. CCF-0207673.

Disclaimer: Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.