Burrows-Wheeler Transform

November 1, 2022

Coding & Algorithm Interview 

Introduction

Data compression is a crucial aspect of modern computing, as it allows for efficient storage and transmission of data. One powerful data compression technique is the Burrows-Wheeler Transform (BWT), which is widely used in various applications, such as file compression, data transmission, and text encoding. In this tech blog, we will delve into the details of the Burrows-Wheeler Transform, how it works, its advantages, and its implementation in code.

What is the Burrows-Wheeler Transform?

The Burrows-Wheeler Transform is a data transformation algorithm that reorganizes a string of characters into a more compressible form by rearranging its characters based on their neighbouring characters. The transformed string typically exhibits a higher degree of repetition and locality, which makes it more amenable to compression using techniques like run-length encoding or entropy coding. The BWT is a reversible process, meaning that the original string can be perfectly reconstructed from the transformed string.

How Does the Burrows-Wheeler Transform Work?

The Burrows-Wheeler Transform operates on a given input string and consists of the following steps:

1. Circular rotations: Create a list of all possible circular rotations of the input string, where each rotation is obtained by cyclically shifting the string to the right.
2. Sorting: Sort the list of circular rotations lexicographically, which means arranging them in dictionary order.
3. Last column: Extract the last character from each sorted rotation and concatenate them to form the transformed string.

The transformed string, obtained after the Burrows-Wheeler Transform, is often significantly different from the original input string, with potentially more repetitions and locality, making it suitable for compression.

Advantages of the Burrows-Wheeler Transform

1. High Compression Ratios: The Burrows-Wheeler Transform can achieve high compression ratios for certain types of data, especially text files with repeated patterns or localized structures.
2. Reversibility: The BWT is a reversible process, meaning that the original input string can be perfectly reconstructed from the transformed string without any loss of information.
3. Simplicity: The BWT is a relatively simple algorithm that can be implemented efficiently with low computational overhead.

Implementation in Code

Here’s a simple implementation of the Burrows-Wheeler Transform in Python:

def burrows_wheeler_transform(s):
    # Step 1: Generate all circular rotations
    rotations = [s[i:] + s[:i] for i in range(len(s))]

    # Step 2: Sort the rotations
    rotations.sort()

    # Step 3: Extract last column
    transformed_string = ''.join(r[-1] for r in rotations)

    return transformed_string

Conclusion

The Burrows-Wheeler Transform is a powerful data compression technique that reorganizes input strings into a more compressible form. It offers advantages such as high compression ratios, reversibility, and simplicity in implementation. It is widely used in various applications, including file compression, data transmission, and text encoding. Understanding the Burrows-Wheeler Transform can be valuable for developers and data scientists working on data compression or related areas in computer science.