Resizing and Rehashing in Hash Tables: Optimizing Performance and Efficiency

5.2.3 Resizing and Rehashing

Hash tables are a fundamental data structure in computer science, providing efficient key-value storage and retrieval. However, as the number of elements in a hash table grows, so does the potential for collisions, which can degrade performance. This section delves into the concepts of resizing and rehashing, essential techniques for maintaining the efficiency of hash tables. By understanding these processes, you’ll be equipped to implement dynamic resizing in your JavaScript hash table class, ensuring optimal performance even as your data grows.

Understanding the Need for Resizing

As elements are added to a hash table, the likelihood of collisions increases if the table’s size remains constant. Collisions occur when multiple keys hash to the same index, leading to longer chains or more probing, which in turn slows down operations like insertion, deletion, and lookup. To mitigate this, we introduce the concept of resizing the hash table.

The Load Factor

The load factor is a critical metric in determining when to resize a hash table. It is defined as the ratio of the number of entries to the number of buckets (slots) in the hash table:

A common threshold for the load factor is 0.7. When the load factor exceeds this threshold, it indicates that the hash table is becoming too full, and resizing is necessary to maintain performance.

Implementing Resizing and Rehashing

Resizing involves creating a new, larger hash table and rehashing all existing keys to the new table. This process can be broken down into several steps:

1. Create a New Larger Array: Typically, the new array is twice the size of the current one. Choosing a prime number for the new size can help reduce collisions.

2. Rehash Existing Keys: Each key-value pair from the old table is rehashed and inserted into the new table.

3. Update References: The hash table’s internal reference is updated to point to the new array.

Let’s implement this in JavaScript:

class HashTable {
  constructor(size = 53) {
    this.keyMap = new Array(size);
    this._count = 0;
  }

  _hash(key) {
    let total = 0;
    let WEIRD_PRIME = 31;
    for (let i = 0; i < Math.min(key.length, 100); i++) {
      let char = key[i];
      let value = char.charCodeAt(0) - 96;
      total = (total * WEIRD_PRIME + value) % this.keyMap.length;
    }
    return total;
  }

  set(key, value) {
    let index = this._hash(key);
    if (!this.keyMap[index]) {
      this.keyMap[index] = [];
    }
    this.keyMap[index].push([key, value]);
    this._count++;

    // Check load factor and resize if necessary
    if (this._count / this.keyMap.length > 0.7) {
      this.resize();
    }
  }

  resize() {
    let oldKeyMap = this.keyMap;
    this.keyMap = new Array(this.keyMap.length * 2);
    this._count = 0;
    for (let bucket of oldKeyMap) {
      if (bucket) {
        for (let [key, value] of bucket) {
          this.set(key, value);
        }
      }
    }
  }

  get(key) {
    let index = this._hash(key);
    if (this.keyMap[index]) {
      for (let [k, v] of this.keyMap[index]) {
        if (k === key) {
          return v;
        }
      }
    }
    return undefined;
  }
}

Rehashing Process

When resizing, each key must be rehashed to determine its new position in the larger array. This is necessary because the hash function depends on the array’s length, which changes during resizing. Rehashing ensures that each key is correctly placed in the new array, maintaining the hash table’s efficiency.

Trade-Offs Between Space and Time

Resizing and rehashing come with trade-offs:

• Time Complexity: Resizing is an expensive operation, with a time complexity of \(O(n)\), where \(n\) is the number of entries in the hash table. However, this operation is infrequent, and the average time complexity for hash table operations remains constant, \(O(1)\).

• Space Complexity: Doubling the size of the hash table increases its memory usage. However, this is necessary to maintain efficient operations and reduce the likelihood of collisions.

Best Practices for Resizing

1. Choose a Prime Number for New Size: This reduces the likelihood of collisions by ensuring a more even distribution of keys.

2. Monitor the Load Factor: Regularly check the load factor and resize before performance degrades.

3. Balance Between Resizing Frequency and Memory Usage: Resizing too often can lead to excessive memory usage, while infrequent resizing can degrade performance.

Conclusion

Resizing and rehashing are crucial for maintaining the efficiency of hash tables as they grow. By understanding the load factor and implementing dynamic resizing, you can ensure that your hash table performs optimally, even with large datasets. This balance between space and time complexity is a key consideration in designing efficient data structures.

Visualizing the Resizing Process

To better understand the resizing process, consider the following diagram illustrating the transition from an old hash table to a new, larger one:

    graph TD;
	    A[Old Hash Table] -->|Rehash Keys| B[New Larger Hash Table];
	    A --> C[Old Bucket 1];
	    A --> D[Old Bucket 2];
	    C -->|Rehash| B;
	    D -->|Rehash| B;

This diagram shows how each bucket in the old hash table is rehashed and inserted into the new table, ensuring that all keys are correctly placed.

Further Reading and Resources

For more in-depth information on hash tables and their implementation, consider the following resources:

• JavaScript Data Structures and Algorithms: An Introduction to Understanding and Implementing Algorithms
• Hash Table Wikipedia
• MDN Web Docs: Working with Objects
• Open Source Hash Table Implementations

By mastering resizing and rehashing, you’ll be well-equipped to handle large datasets efficiently, ensuring that your applications remain performant and responsive.

Quiz Time!