How to Efficiently Calculate Hamming Distance on Binary Strings in SQL?

Hamming Distance on Binary Strings in SQL

Background and Problem Statement

The Hamming distance, a fundamental concept in computer science, measures the dissimilarity between two binary strings by counting the number of differing bits. In SQL, it becomes necessary to compute Hamming distances for various purposes, such as finding similar or nearest neighbor data points.

The Challenge

A developer encounters a hurdle while attempting to calculate the Hamming distance between entries in a table's binary column and a supplied value. The issue lies with the inherent limitations of SQL's integer-based operators and functions, which are incompatible with binary strings.

Solutions Explored

1. Substring and Integer Operation Approach

The developer considers manually breaking down the binary strings into substrings, converting each to integers, and calculating the Hamming distance substring-wise. However, this approach is complex, inefficient, and not elegant.

2. Storing Hash in Multiple BIGINT Columns

Subsequent research reveals that storing the hash in four BIGINT columns, each representing an 8-byte substring, significantly accelerates the Hamming distance computation. The developer creates a custom function that combines the Hamming distances of each substring.

Function Implementation

<code class="sql">CREATE FUNCTION HAMMINGDISTANCE(
  A0 BIGINT, A1 BIGINT, A2 BIGINT, A3 BIGINT, 
  B0 BIGINT, B1 BIGINT, B2 BIGINT, B3 BIGINT
)
RETURNS INT DETERMINISTIC
RETURN 
  BIT_COUNT(A0 ^ B0) +
  BIT_COUNT(A1 ^ B1) +
  BIT_COUNT(A2 ^ B2) +
  BIT_COUNT(A3 ^ B3);</code>

This approach demonstrates over 100-fold performance improvements in testing compared to the binary column-based calculation.

Alternative Approach with String Conversion

In an alternative approach, the developer converts the binary substrings to hexadecimal values, further converts them to decimals, and then computes the Hamming distance using bitwise XOR and BIT_COUNT. This approach, however, involves several conversion steps, making it less efficient than the BIGINT column-based method.

Conclusion

The customization and usage of multiple BIGINT columns offer a fast and efficient solution to calculating Hamming distances on binary strings in SQL. This approach is especially advantageous when dealing with large datasets, where performance becomes critical.

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