Hash tables are really important in today's computing world. They help us quickly find and access information. But sometimes, problems come up when two items try to go into the same spot in the table. This is known as a collision. To fix this issue, there are different methods or techniques to improve how hash tables work.

Common Collision Resolution Techniques:

1. Chaining:

   • This method keeps a list of items for each spot in the hash table. When a collision happens, the new item is added to the list at that spot.
   • Example: Think about a hash table for students, where Alice (ID 123) and Bob (ID 456) both go to the same index 7. Instead of replacing the info, we create a list at index 7: 7 -> Alice -> Bob.

2. Open Addressing:

   • With this method, all items go directly into the hash table. If a collision occurs, the system looks for the next open spot.
   • Example: If Alice hashes to index 7 and it’s taken, the system checks index 8 next. If that one is busy too, it moves to index 9, and keeps going until it finds an empty spot.

3. Double Hashing:

   • This is a fancy version of open addressing. It uses a second hash function to decide how far to move when looking for a new spot.
   • Example: If Alice goes to index 7 and it’s full, her next spot could be calculated using a formula like $(7 + h2(123)) \mod N$, where $h2$ is the second hash function.

Performance Enhancement:

Using these techniques, hash tables stay efficient, even as they get bigger. Chaining makes it easy to add more entries without losing any information. Open addressing keeps all items in the table, which is helpful. This flexibility is especially important when we have a lot of data. It ensures that finding, adding, and removing items usually takes the same amount of time, around $O(1)$, which is super quick.

In short, collision resolution techniques are really important for improving hash tables. They help make hash tables work well for many uses in computer science, like in databases and caches.