Introduction

An Incremental Directed Acyclic Word Graph (DAWG) is a powerful data structure that efficiently handles storing and searching strings. It is particularly useful when you are dealing with large datasets of strings, such as in text processing, when you want to build a compact representation for a dictionary or lexicon. This article aims to guide you through constructing an incremental DAWG and understanding its internal workings.

Directed Acyclic Word Graph: Overview

A Directed Acyclic Word Graph (DAWG) is a minimized trie of a given set of strings. Unlike a traditional trie, DAWG merges equivalent nodes, reducing redundancy. Since DAWG is acyclic and directed, it offers an optimized space complexity for dynamic string collections.

Key Characteristics of DAWG

• Acyclic: DAWG has no cycles.
• Directed: Follow node connections in only one direction from root to leaf nodes.
• Minimized: Redundant nodes are merged, reducing the overall size compared to a traditional trie.

Constructing an Incremental DAWG

Creating an incremental DAWG involves adding strings one by one to the graph and minimizing on-the-fly. Let's delve into the steps to construct an incremental DAWG:

Step 1: Initial Setup

Begin with an empty DAWG, starting with a single root node. All strings start from this root.

• "b" would be a new branch from the root.
• "at" shares the same suffix with "cat", so nodes for "a" and "t" can be merged.
• Traverse the graph from the root by following edges labeled with input characters.
• If the path exists for the whole input string, the string is present.
• Space-efficient: Merges common prefixes and suffixes, reducing duplication.
• Fast Search: Path traversal augments efficient string lookup.
• Incremental Update: Can add strings dynamically without rebuilding the entire graph.
• Complex Implementation: Ensures correct and efficient merging is non-trivial.
• Overhead: The additional complexity of merging can introduce an overhead in insertion times.