Introduction

The problem of finding and removing "almost duplicate" strings from a dataset is a common challenge in text processing and data cleaning. In computational terms, an "almost duplicate" string is typically defined with a threshold representing a minimal permissible difference in terms of edits (`Levenshtein distance`), character similarity, or subsequence matching. Given this complexity, achieving subquadratic time complexity in processing large datasets is crucial for efficiency.

Problem Definition

Given a set of strings, the task is to identify and remove strings that are "almost duplicates" of one another, ensuring that the remaining set is unique within specified tolerances. Assume the set of strings is denoted as $S = {s_1, s_2, \ldots, s_n}$. The objective is to determine a subset $S'$ such that no two strings in $S'$ are almost duplicates according to specified criteria.

Traditional Approaches

1. Brute Force Comparison:
   Perform pairwise comparisons of all strings to identify duplicates, which results in $O(n^2)$ time complexity.
2. Sorting and Comparison:
   Sort strings followed by adjacent comparison, often reducing complexity slightly but still remaining quadratic concerning the total number of strings.
3. Hashing Techniques:
   Utilizing hash maps to store encountered strings and their modified forms, allowing faster lookups.

Each traditional approach has its own merits and demerits, but often falls short of achieving subquadratic time complexity, especially for large datasets.

Enhanced Subquadratic Approach

Overview

To achieve subquadratic time complexity, let's consider an approach that blends hashing with efficient data structures for pattern matching and similarity measurement. The main idea revolves around efficiently indexing strings and exploiting their structural properties.

Key Techniques

1. Locality-Sensitive Hashing (LSH):
   Use LSH to map strings to hash buckets such that "almost duplicate" strings fall into the same bucket with high probability. The hash function is designed to be sensitive to the chosen similarity metric. This reduces the number of pairwise comparisons drastically.
2. Tries & Suffix Arrays:
   Utilize data structures like `tries` or `suffix arrays` to quickly evaluate edit distances or common sub-sequences. These structures speed up similarity searches and sub-sequence checks.
3. Dynamic Programming for Distance Calculation:
   Implement an optimized dynamic programming approach to calculate the edit distance, leveraging previous computations stored in a memorization array.

Example

To illustrate, consider strings of limited length, using a simplified edit distance threshold. Two strings are considered almost duplicates if their edit distance is $\leq 1$. Here's a step-by-step breakdown:

1. Insert Strings into a Trie: