Introduction

A hashtable is an efficient data structure used for storing and retrieving data based on key-value pairs. It is widely known for providing average-case constant time complexity, $O(1)$, for both insertion and retrieval operations. However, like other data structures, hashtables have certain limitations. When used with simple linked lists, they can suffer from performance issues when dealing with high-collision scenarios. The integration of doubly linked lists can help mitigate these issues by providing better traversal efficiency and memory management.

How a Hashtable Works

A hashtable associates keys with values using a hash function. The hash function maps keys to indices in an array, known as the "hash table." Each index can store one or more key-value pair(s). In cases where two keys hash to the same index, a collision occurs, which is typically resolved using methods such as chaining or open addressing. This article focuses on chaining, particularly using doubly linked lists.

Chaining with Doubly Linked Lists

In a typical hashtable using chaining, secondary data structures such as linked lists store multiple key-value pairs at each index of the table to manage collisions. A doubly linked list provides additional benefits over a singly linked list:

1. Bidirectional Traversal:
   • A doubly linked list allows traversal in both forward and backward directions. This flexibility provides faster access for certain operations such as deletion or finding the previous key, improving the efficiency of these operations within the hashtable.
2. Ease of Deletion:
   • With doubly linked lists, each node contains pointers to both the next and previous nodes. This feature eliminates the need for maintaining a trail node, which is required in singly linked lists to achieve efficient deletion.
3. Complexity Management:
   • Particular scenarios, such as high collision instances, where many keys hash to the same index, can be better managed using a doubly linked list. The distributed pointer references help in optimizing memory and time complexity.

Technical Explanation

Consider a hashtable H with size $N$, where each bucket is a doubly linked list. Below is the typical node structure for a doubly linked list used within the hashtable:

• Efficiency in Deletion and Updates:
• Enhanced Access:
• Extra Memory Overhead:
• Increased Complexity:
• LRU (Least Recently Used) Cache:
• Order-sensitive Datasets: