Algorithms on Strings

Go to Course: https://www.coursera.org/learn/algorithms-on-strings

Introduction

### Course Review: Algorithms on Strings #### Overview In an age dominated by a deluge of textual information, understanding how to efficiently process and analyze strings is invaluable. The "Algorithms on Strings" course on Coursera delves into the world of string algorithms, shedding light on their application in search engines and personalized medicine. This course is perfect for anyone looking to enhance their knowledge of algorithmic techniques crucial for string processing. #### Course Structure The course is meticulously structured around four key modules, each designed to build upon the concepts introduced in the previous ones. 1. **Suffix Trees** - The journey begins with an introduction to suffix trees, a fundamental data structure for efficient pattern matching. You will learn about Peter Weiner's groundbreaking algorithm from 1973, which demonstrated how to find the longest repeat in a string in linear time. This foundation sets the stage for more advanced concepts and applications. 2. **Burrows-Wheeler Transform and Suffix Arrays** - This module explores the revolutionary Burrows-Wheeler Transform (BWT), originally intended for text compression. You’ll discover how BWT unexpectedly became crucial in genomics for identifying disease-causing mutations, exemplifying the unpredictable applications of algorithms. This section of the course beautifully illustrates the connection between text processing and biological data analysis. 3. **Knuth-Morris-Pratt Algorithm** - After laying the groundwork, the course introduces the Knuth-Morris-Pratt (KMP) algorithm. This is where things get intriguing as it explains how to achieve exact pattern matching in linear time. Understanding this concept deepens your comprehension of string processing and is foundational for the ensuing modules. 4. **Constructing Suffix Arrays and Suffix Trees** - The final module shifts focus towards practical implementation. You’ll learn efficient algorithms for constructing suffix arrays and trees, including an O(n log n) suffix array construction algorithm and a linear time approach for suffix tree construction from a suffix array. The hands-on approach, especially the programming assignments, encourages active engagement with the content. #### Recommendations If you have a background in computer science or mathematics, this course is highly recommended. It provides solid theoretical knowledge paired with practical implementation, making it an essential learning experience for aspiring data scientists, software engineers, or researchers in bioinformatics. The insights gained from studying string algorithms can be applied in numerous fields where text processing is key, including search engines, natural language processing, and data analysis in the healthcare sector. #### Conclusion "Algorithms on Strings" is not just an academic endeavor but a gateway into understanding how string algorithms play a critical role in various technologies that shape our world today. By the end of this course, you will possess a robust foundation in string algorithms, empowering you with the skills necessary to tackle complex string matching and processing problems. Whether you’re interested in pursuing a career in tech or enhancing your programming repertoire, this course is an excellent investment in your future. Don't hesitate to enroll and start your journey into the fascinating world of algorithms!

Syllabus

Suffix Trees

How would you search for a longest repeat in a string in LINEAR time? In 1973, Peter Weiner came up with a surprising solution that was based on suffix trees, the key data structure in pattern matching. Computer scientists were so impressed with his algorithm that they called it the Algorithm of the Year. In this lesson, we will explore some key ideas for pattern matching that will - through a series of trials and errors - bring us to suffix trees.

Although EXACT pattern matching with suffix trees is fast, it is not clear how to use suffix trees for APPROXIMATE pattern matching. In 1994, Michael Burrows and David Wheeler invented an ingenious algorithm for text compression that is now known as Burrows-Wheeler Transform. They knew nothing about genomics, and they could not have imagined that 15 years later their algorithm will become the workhorse of biologists searching for genomic mutations. But what text compression has to do with pattern matching??? In this lesson you will learn that the fate of an algorithm is often hard to predict – its applications may appear in a field that has nothing to do with the original plan of its inventors.

Congratulations, you have now learned the key pattern matching concepts: tries, suffix trees, suffix arrays and even the Burrows-Wheeler transform! However, some of the results Pavel mentioned remain mysterious: e.g., how can we perform exact pattern matching in O(|Text|) time rather than in O(|Text|*|Pattern|) time as in the naïve brute force algorithm? How can it be that matching a 1000-nucleotide pattern against the human genome is nearly as fast as matching a 3-nucleotide pattern??? Also, even though Pavel showed how to quickly construct the suffix array given the suffix tree, he has not revealed the magic behind the fast algorithms for the suffix tree construction!In this module, Miсhael will address some algorithmic challenges that Pavel tried to hide from you :) such as the Knuth-Morris-Pratt algorithm for exact pattern matching and more efficient algorithms for suffix tree and suffix array construction.

In this module we continue studying algorithmic challenges of the string algorithms. You will learn an O(n log n) algorithm for suffix array construction and a linear time algorithm for construction of suffix tree from a suffix array. You will also implement these algorithms and the Knuth-Morris-Pratt algorithm in the last Programming Assignment in this course.