Handling Collisions in Hash Tables

A collision occurs in a hash table when two different keys map to the same index after applying the hash function. Since hash functions have a finite output range, collisions are unavoidable in practice.

Efficient collision handling is what allows hash tables to maintain fast average-case performance.

Why Collisions Happen

Collisions occur because:

• The number of possible keys is larger than the number of buckets
• Different keys can produce the same hash value
• Poor hash functions increase collision frequency

hash("key1") → 2
hash("key2") → 2   ← collision

What Happens Without Collision Handling?

If collisions were not handled:

• Data would be overwritten
• Lookups would return incorrect values
• The hash table would become unusable

Therefore, collision resolution is a core requirement of any hash table implementation.

Collision Resolution Strategies

There are two primary strategies for handling collisions:

1. Separate Chaining
2. Open Addressing

1. Separate Chaining

Idea

Each bucket holds a collection (usually a linked list) of key-value pairs.

Index 3:
("cat", 1) → ("dog", 4) → ("cow", 2)

If multiple keys hash to the same index, they are stored together.

Advantages

• Simple to implement
• Easy deletion
• Performance degrades gracefully

Disadvantages

• Extra memory for pointers
• Poor cache locality

2. Open Addressing

Idea

When a collision occurs, the algorithm probes for another empty slot.

Index 2 → occupied
Index 3 → occupied
Index 4 → free → insert

All elements are stored directly in the table.

Common Probing Techniques

Linear Probing

index, index+1, index+2, ...

Quadratic Probing

index + 1², index + 2², ...

Double Hashing

index + i * hash2(key)

Advantages

• Better cache performance
• No extra memory for pointers

Disadvantages

• Deletion is complex
• Clustering can degrade performance

Load Factor

The load factor determines how full the table is:

load factor = entries / buckets

As the load factor increases:

• Collisions become more frequent
• Performance degrades

Hash tables resize automatically to keep the load factor within a safe range.

How Rust’s HashMap Handles Collisions

Rust’s HashMap:

• Uses hashing + probing techniques
• Employs a randomized hashing algorithm to prevent attacks
• Automatically resizes to maintain performance

The exact details are abstracted away, but collision handling is fully automatic.

Collision Handling and Performance

In practice, good hashing keeps performance near constant time.

Why You Rarely Worry About Collisions

Modern hash map implementations:

• Use strong hash functions
• Resize dynamically
• Balance memory and speed automatically

Understanding collisions is important conceptually, but most applications rely on well-tested libraries.

Summary

• Collisions are unavoidable in hash tables
• Must be handled correctly for correctness and performance
• Two main strategies: chaining and open addressing
• Load factor strongly influences performance
• Rust’s HashMap handles collisions internally