Question

Can you think of techniques other than chaining to handle bucket overflow in external hashing?

Short answer

Open addressing, inclusive of variations such as linear probing, quadratic probing, and double hashing, is an alternative handling method for bucket overflow in external hashing, apart from chaining.

Step-by-step solution

Understanding External Hashing and Overflow

Techniques are needed to handle bucket overflow in external hashing since each bucket in a hash table is typically allotted a fixed amount of space, and an overflow may occur if a bucket needs to store more entries than it can handle. Overflow typically occurs when the hash function used results in 'collisions'. These are instances where two or more keys map to the same bucket.

Common Overflow Handling Approach: Chaining

Chaining is a commonly used technique to handle bucket overflow. In chaining, each bucket in the hash table is extended to a linked list. Each linked list holds all the elements that hash to the same bucket. So, when an element needs to be inserted that hashes to a full bucket, it is added to the end of the identified bucket's linked list. The issue with chaining is that it can lead to long linked lists, thus slowing down access time.

Alternative Overflow Handling Approach: Open Addressing

An alternative to chaining is a group of methods referred to as open addressing. In open addressing, all elements are stored in the hash table itself. So when a new record needs to be inserted, the buckets are examined, starting with the hashed-to slot and proceeding in a predefined sequence, until an unoccupied slot is found. When searching for a record, we systematically probe the table until we find a record with the given key or it is clear that the record is not in the table. Variations of this method include linear probing, quadratic probing, and double hashing.

Key concepts

Chaining

The idea of chaining as an overflow handling method in external hashing lies in its simplicity and effectiveness. It involves pairing each bucket with a linked list or chain. Whenever a hash function leads to a collision—multiple keys mapping to the same bucket—instead of panicking that the 'inn' is full, we simply add the newcomer to this chain. Imagine a cloakroom where, instead of a single hook, you have a small rail where multiple coats can hang. In the context of hash tables, instead of coats, we have data entries.

Why is chaining embraced by many? Mainly because it makes allowances for an unlimited number of collisions by letting each bucket grow indefinitely. Of course, with great size comes greater search time, which can be a drawback if not managed well. The longer the chain, the longer it takes to traverse it when you're searching for a particular 'coat' in a sea of similar ones.

Open Addressing

On the other hand, open addressing is like playing a game of musical chairs with data. There's a finite number of chairs, or buckets, to begin with, and every music stop—a collision—means data must find the next free seat. The whole hash table is leveraged, meaning that instead of adding extra structures like chains, we probe around for available space within the table.

Imagine a parking lot—all spots are taken, yet, there’s this one car (data) roaming around looking for any empty slot. The benefit of this method is that it saves memory since there's no need for extra data structures like the chains mentioned earlier. However, the catch is that as the table fills up, finding a free slot becomes more challenging. It's also important that the table never becomes completely full, or else the parking lot scenario becomes a real headache for the new arrival.

Collision Resolution

Collisions are like having two people claim the same seat. Uncomfortable, right? In hashing, this occurs when two keys yield the same address. Collision resolution techniques, therefore, are methods of dealing with this overlap so that the data can live together harmoniously in the hash table. An efficient resolution strategy is not only about finding a free spot but also ensuring that future searches are not unduly slowed down by the solution you've chosen.

Choosing the right collision resolution technique is pivotal. Just as in a game of seating arrangement logistics, if you have a poorly thought-out plan, your guests (or data) will end up frustrated, shuffling around aimlessly.

Linear Probing

Linear probing is the simplest form of open addressing. When a collision occurs, it deals with this by checking the next bucket. And if that's occupied? Well, move on to the next and so on, in a linear sequence. Think hopscotch, but instead of a stone, you're hopping a data entry along until it finds an open spot.

While simple and intuitive, this technique can lead to clustering—where a group of consecutive spaces gets filled up, leading to longer search times. It's sort of like the bus in rush hour; eventually, passengers (data points) end up crowded together, and the next person getting on has to squeeze through.

Quadratic Probing

Enter quadratic probing, a close cousin of linear probing but with a fancy twist. Instead of searching in a straight line, quadratic probing searches in a quadratic manner to find a free bucket. This means that the distance between the slots being checked increases exponentially—it's like taking ever-larger steps down the hash table.

What's the advantage? It significantly reduces clustering and spreads entries more evenly across the table. Sure, envisioning the hopscotch analogy from earlier, but each hop now is longer than the last. It's a bouncing ball that gradually covers more ground with each bounce.

Double Hashing

Double hashing is the superhero of collision resolution methods. It uses not one, but two hash functions. When a collision occurs, the second hash function kicks in to calculate an interval for probing, differing from the linear or quadratic approaches previously discussed.

Double hashing is akin to using a combination of two different secret knocks to enter a hidden clubhouse—the complexity of two layers making it much harder for overlaps to occur. It's a powerful method because it minimizes clustering and provides a much better distribution, ensuring a game of data musical chairs with more sophistication and far fewer collisions.