We strongly recommend referring below post as a prerequisite of this.
Hashing | Set 1 (Introduction)
Hashing | Set 2 (Separate Chaining)

Open Addressing
Like separate chaining, open addressing is a method for handling collisions. In Open Addressing, all elements are stored in the hash table itself. So at any point, the size of the table must be greater than or equal to the total number of keys (Note that we can increase table size by copying old data if needed).

Along with quadratic probing and double hashing, linear probing is a form of open addressing.In these schemes, each cell of a hash table stores a single key–value pair. When the hash function causes a collision by mapping a new key to a cell of the hash table that is already occupied by another key, linear probing searches the table for the closest following free location and inserts the new. Jul 06, 2018 Let’s try and apply the linear probing method now. What we want to do is take the data that has collided and walk the other one down the array until it finds the next available slot.

Under linear probing, we look sequentially, slot by slot, until we find an open position. In this case, we find slot 1. Again, 55 should go in slot 0 but must be placed in slot 2 since it is the next open position. The final value of 20 hashes to slot 9.

Insert(k): Keep probing until an empty slot is found. Once an empty slot is found, insert k.

Search(k): Keep probing until slot’s key doesn’t become equal to k or an empty slot is reached.

Delete(k): Delete operation is interesting. If we simply delete a key, then the search may fail. So slots of deleted keys are marked specially as “deleted”.
The insert can insert an item in a deleted slot, but the search doesn’t stop at a deleted slot.

Open Addressing is done in the following ways:

a) Linear Probing: In linear probing, we linearly probe for next slot. For example, the typical gap between two probes is 1 as taken in below example also.
let hash(x) be the slot index computed using a hash function and S be the table size

Let us consider a simple hash function as “key mod 7” and sequence of keys as 50, 700, 76, 85, 92, 73, 101.

Challenges in Linear Probing :

1. Primary Clustering: One of the problems with linear probing is Primary clustering, many consecutive elements form groups and it starts taking time to find a free slot or to search an element.
2. Secondary Clustering: Secondary clustering is less severe, two records do only have the same collision chain(Probe Sequence) if their initial position is the same.

b) Quadratic Probing We look for i²‘th slot in i’th iteration.

c) Double Hashing We use another hash function hash2(x) and look for i*hash2(x) slot in i’th rotation.

See this for step by step diagrams.

Linear Probing Looks For The Next Free Slot Machines

Comparison of above three:
Linear probing has the best cache performance but suffers from clustering. One more advantage of Linear probing is easy to compute.
Quadratic probing lies between the two in terms of cache performance and clustering.
Double hashing has poor cache performance but no clustering. Double hashing requires more computation time as two hash functions need to be computed.

Linear Probing Looks For The Next Free Slot Extruded

Performance of Open Addressing:
Like Chaining, the performance of hashing can be evaluated under the assumption that each key is equally likely to be hashed to any slot of the table (simple uniform hashing)

Linear Probing Looks For The Next Free Slot Games

References:
http://courses.csail.mit.edu/6.006/fall11/lectures/lecture10.pdf
https://www.cse.cuhk.edu.hk/irwin.king/_media/teaching/csc2100b/tu6.pdf

Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.

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