Collision Resolution Techniques

In Hashing, hash functions were used to generate hash values. The hash value is used to create an index for the keys in the hash table. The hash function may return the same hash value for two or more keys. When two or more keys have the same hash value, a collision happens. To handle this collision, we use Collision Resolution Techniques.

Collision Resolution Techniques

There are mainly two methods to handle collision:

1. Separate Chaining
2. Open Addressing

1) Separate Chaining

The idea behind Separate Chaining is to make each cell of the hash table point to a linked list of records that have the same hash function value. Chaining is simple but requires additional memory outside the table.

Example: We have given a hash function and we have to insert some elements in the hash table using a separate chaining method for collision resolution technique.

Hash function = key % 5,
Elements = 12, 15, 22, 25 and 37.

Let’s see step by step approach to how to solve the above problem:

Please You Own Hash Table with Chaining for implementation of this technique

2) Open Addressing

In open addressing, all elements are stored in the hash table itself. Each table entry contains either a record or NIL. When searching for an element, we examine the table slots one by one until the desired element is found or it is clear that the element is not in the table.

2.a) Linear Probing

In linear probing, the hash table is searched sequentially that starts from the original location of the hash. If in case the location that we get is already occupied, then we check for the next location.

Algorithm:

1. Calculate the hash key. i.e. key = data % size
2. Check, if hashTable[key] is empty
   • store the value directly by hashTable[key] = data
3. If the hash index already has some value then
   • check for next index using key = (key+1) % size
4. Check, if the next index is available hashTable[key] then store the value. Otherwise try for next index.
5. Do the above process till we find the space.

Example: Let us consider a simple hash function as “key mod 5” and a sequence of keys that are to be inserted are 50, 70, 76, 85, 93.

Please refer Your Own Hash Table with Linear Probing in Open Addressing for implementation details.

2.b) Quadratic Probing

Quadratic probing is an open addressing scheme in computer programming for resolving hash collisions in hash tables. Quadratic probing operates by taking the original hash index and adding successive values of an arbitrary quadratic polynomial until an open slot is found.

An example sequence using quadratic probing is:

H + 1 ² , H + 2 ² , H + 3 ² , H + 4 ² …………………. H + k ²

This method is also known as the mid-square method because in this method we look for i²-th probe (slot) in i-th iteration and the value of i = 0, 1, . . . n – 1. We always start from the original hash location. If only the location is occupied then we check the other slots.

Let hash(x) be the slot index computed using the hash function and n be the size of the hash table.

If the slot hash(x) % n is full, then we try (hash(x) + 1 ² ) % n.
If (hash(x) + 1 ² ) % n is also full, then we try (hash(x) + 2 ² ) % n.
If (hash(x) + 2 ² ) % n is also full, then we try (hash(x) + 3 ² ) % n.
This process will be repeated for all the values of i until an empty slot is found

Example: Let us consider table Size = 7, hash function as Hash(x) = x % 7 and collision resolution strategy to be f(i) = i ² . Insert = 22, 30, and 50

Please refer Your Own Hash Table with Quadratic Probing in Open Addressing for implementation.

2.c) Double Hashing

Double hashing is a collision resolving technique in Open Addressed Hash tables. Double hashing make use of two hash function,

• The first hash function is h1(k) which takes the key and gives out a location on the hash table. But if the new location is not occupied or empty then we can easily place our key.
• But in case the location is occupied (collision) we will use secondary hash-function h2(k) in combination with the first hash-function h1(k) to find the new location on the hash table.

This combination of hash functions is of the form

h(k, i) = (h1(k) + i * h2(k)) % n

where

• i is a non-negative integer that indicates a collision number,
• k = element/key which is being hashed
• n = hash table size.

Complexity of the Double hashing algorithm:

Time complexity: O(n)

Example: Insert the keys 27, 43, 692, 72 into the Hash Table of size 7. where first hash-function is h1​(k) = k mod 7 and second hash-function is h2(k) = 1 + (k mod 5)

Please refer Double Hashing for Implementation.