Fibonacci Hashing and Fastest Hashtable

 Fibonacci Hashing and Fastest Hashtable

Before we get into Fibonacci hashing and the fastest hashtable, let's understand what hash and hashtable are and their role in a data structure.

What is called hashing?

In the data structure, "hashing" is the method of mapping a large volume of the database into small tables using a hash function. It is also called the Message Digest feature. It is a technique that uniquely identifies items from a collection of similar terms.

Hashing uses hash tables to store data in array format. Each of the values in the array has allotted a unique index number. Hash tables use a method to generate unique index numbers for each value stored in an array format. This method is also known as the hash method or technique.

Hashing types in a data structure is a two-step process: 

1. A hash function will convert items to small integers or hash values. The original data can be stored by using an index in this integer.

2. In a hashtable you can store data. You can also find data quickly and faster by using the hash key.

Real-life based examples of hashing in a data structure

In schools, teachers assign each student a unique number. The teacher will use this number to retrieve information related to that student.

The library has an uncountable amount of books. The librarian gives a unique number or Id to each book. This unique number helps in finding the actual position of the books on the shelf as well as who is borrowing the books from the library.

Hash function

A hash function in a data structure maps arbitrary-size data to fixed-size data. It gives back the following values: small integer (also known as hash value), hash codes, and hash sums. The hashing techniques in the data structure are very engaging, such as:

hash=hashfunc(key)

index=hash%array_size

The hash function covers the following requirements:

• A good hash function is easy to compute.
• A good hash function never gets stuck in the cluster and distributes the keys evenly across the hash table.
• A good hash function prevents a collision when two elements or items are assigned the same hash value.

The three characteristics of a hash function in a data structure are:

• Puzzle friendly
• The property to be hidden
• No collision

Hashtable

In a data structure hashing uses a hash table to store key-value pairs. The hash table uses a hash function to create an index. A unique index is used by hashing to execute, insert, update and search operations.

It can be defined as a segment where data is stored in array format. This data has its own index value. If the index values ​​are known, the data access process is faster.

How does hashing work in a data structure?

When hashing, a hash function maps a string or number to a small integer. Hash tables retrieve an item from a list using a hash function. The goal of the hashing technique is to distribute the data evenly across the array. Hashing assigns a unique key to all elements. The hashtable uses the key to access the data in the list.

A hash table stores data in a key-value pair. The key is the input to the hash function. The header function then creates a unique index number for each value that is stored. Index numbers store a value that corresponds to a given key. The hash function returns a small integer as output. The output of the hash function is called the hash value.

We further learn that hashtable stores data in an associative manner and data is stored in the form of arrays. Each element in the array has a different index value. Hashtables provide us with the convenience of efficiently searching for the required data. Searching for data and hashtable elements is easy and fast because we can do so by identifying the relevant indexes. Inserting and deleting data in hash tables is done using the hashing method.

About hashing methods

Now that we have a basic understanding of hashing and hashtables, this brings us to our main topic of discussion, Fibonacci hashing. In the real world, Fibonacci hashing is not implemented or used or part of it because it is actually a more expensive method for some reason (time and space).

So let's start to understand the Fibonacci series and how its idea came to implement hashing in a hashtable.

The Fibonacci series is...

F(n) = F(n-1) + F(n-2)

which results in the sequence as

1 1 2 3 5 8 13 21 34 55 89 and so on...

Now, because nature always uses the Fibonacci sequence to develop new things for various reasons, for example in plants, there is always a new leaf coming into the Fibonacci sequence to get the right sunlight. And each successive number of the Fibonacci series follows the golden ratio Φ = 1.6180

example 8/5 = 1.6 and 34/21 = 1.61 and as the number grows it gets more accurate.

Each step around the circle must be at an angle of 360°/8 to get the correct sunlight. Similarly, we can predict the next number of possibilities, then we can take it again on the circle, divided by 360° by the number of possibilities as per the desired space. Using the golden ratio, we can arrange elements to appear randomly distributed without any clusters where structures appear to overlap.

Problems with the Integer modulo method

This method is claimed by programmers as the next fastest method, but in reality, this method is very slow and the input data cannot be evenly distributed to avoid/reduce collisions. It causes problems in creating patterns from given inputs and makes it difficult to run complicated hash functions.

Why is Fibonacci hashing the solution?

• The Fibonacci hash method helps us structure our data faster than other methods. In constant competition, everyone would find faster alternatives. 

• When we search for faster hashtables, we come across google::densehash_map, which is considered to be the fastest hashtable benchmark.

• This fastest hashing method is becoming very unwieldy and time-consuming, and programmers are looking for faster alternatives because time is a valuable resource. Fibonacci hashing is a fair alternative for programmers to consider.

• It's really fast because it's integer multiplication, which saves programmers crucial time. It's also a good idea to run hash functions.

• Although Fibonacci hashing consumes a lot of space to visualize the whole concept, it arranges data conveniently and more conveniently for programmers to locate easily.

• It combines input patterns and gives us infinite data storage without creating any clusters and also avoids wasting space.

Conclusion

Fibonacci hashing is a multiplicative hashing function related to the golden ratio, it is faster than sequential or binary search. Although Fibonacci hashing is not the best hash function, it is better than the integer modulo method. However, it is important to note that this function can cause collisions, so it is better to choose prime numbers carefully. It is also important to note that Fibonacci hashing is not as fast as other hash functions. We are still exploring faster and more convenient methods in the digital world for making the storage of data faster and more advanced way.