Hashing

Hashing• Hashing is the transformation of a

string of characters into a usually shorter fixed-length value or key that represents the original string. Hashing is used to index and retrieve items in a database because it is faster to find the item using the shorter hashed key than to find it using the original value. It is also used in many encryption algorithms.

Hash Table• Is a data structure that

associates keys with values

A small phone book as a hash table.

Hash Table (1)• The primary operation it supports

efficiently is a lookup: given a key (a person's name), find the corresponding value (that person's telephone number). It works by transforming the key using a hash function into a hash, a number that is used as an index in an array to locate the desired location where the values should be.

Hash Function• The hashing algorithm• is any well-defined procedure or

mathematical function which converts a large, possibly variable-sized amount of data into a small datum, usually a single integer that may serve as an index into an array. The values returned by a hash function are called hash values, hash codes, hash sums, or simply hashes.

Hash Function

1.Direct Hashing The key is the address without any algorith-mic manipulation. The data structure must therefore contain an element for every possible key. While the situations where you can use direct hashing are limited, when it can be used it is very powerful because it guarantees that there are no synonyms.

001 Elmer002 Markh

005 Reymund

007 Hubert

100 Rollyn

HashFunction

005100002

5100

2

Address

Key

2.Subtration Method Sometimes we have keys that are

consecutive but do not start from one. Example: A company may have only 100

employees, but the employee numbers start from 1000 and go to 1100. In this case, we use a very simple hashing function that subtracts 1000 from the key to determine the address.

3.Digit Extraction Selected digits are extracted from the key

and used as the address. Example: Using six-digit employee number to

hash to a three-digit address (000-999), we could select the first, third, and fourth digits.

379452 = 394121267 = 112378845 = 388160252 = 102

379452 Elmer

121267 Markh

378845 Hubert

160252 Arno045128 Rollyn

HashFunction

121267045128379452

33071

Divides the key by the array size and uses the remainder + 1

[001]

[006]

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[002]

[007]

[306][307]

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4.Mod division

5.Midsquare Hashing The key is squared and the address

selected from the middle of the squared number.

Example: 9452 * 9452 = 89340304 : address is

3403As a variation, we can select a portion of the key, and then use them rather than the whole key. 379452 : 379 * 379 = 143641 : address is 364 378845 : 378 * 378 = 142884 : address is 288

6.Folding Methods There are two folding methods that are

used: Fold Shift, the key value is divided into

parts whose size matches the size of the required address. Then, the left and right parts are shifted and added with the middle part.

Fold Boundary, the left and right numbers are folded on a fixed boundary between them and the center number. This results in a two outside values being reverse

123456789368

321456987764

1

123456789

1

123 789

Discarded

123

KeyDigits

reversed

789

Digitsreversed

Load Factor Is the number of elements in the list divided by the number of physical elements allocated for the list expressed for a percentage.

a = k / n x 100Clustering The tendency of data to build up unevenly across a hashed list. It is usually created by collisions.

Collision

Collision Is the event that occurs when a hashing algorithm produce an address for an insertion key and that address is already occupied.Home Address The address produced by hashing algorithm.Prime Area The memory that contains all of the home addresses.Probe Calculation of address and test for success.

[1] [5] [9] [17]

1. hash(A)2. hash(B) 3. hash(C)

B & ACollides C & B

Collides

A BC

Collision Resolution • The process of finding alternate location• Collision strategy techniques:

– Separate chaining– Open addressing– Coalesced hashing– Perfect hashing– Dynamic perfect hashing– Probabilistic hashing– Robin hood hashing– Cache-conscious collision resolution

Separate Chaining• Sometimes called simply

chaining or direct chaining, in its simplest form each slot in the array is a linked list, or the head cell of a linked list, where the list contains the elements that hashed to the same location. Insertion requires finding the correct slot, then appending to either end of the list in that slot

Open Addressing• Open addressing hash tables store the records directly

within the array. This approach is also called closed hashing. A hash collision is resolved by probing, or searching through alternate locations in the array (following a probe sequence) until either the target record is found, or an unused array slot is found, which indicates that there is no such key in the table.

Well Known Probe Sequences

379452 Elmer

121267 Markh

378845 Hubert

160252 Arno

045128 Rollyn

HashFunction

070918

166702

Collision is resolved by adding one(1) to the current address

[001]

[006]

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[007]

[306][307]

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Linear Probing

070918 Redjie

166702 Reymund

Quadratic Probing The increment is the collision probe number

squared.Probe Collision Probe2 and New Num Location Increment Address 1 1 12 = 1 1

2 2 22 = 4 33 6 32 = 9 54 15 42 = 16 75 31 52 = 25 96 56 62 = 36 11

Key Offset Is a double hashing method that produces

different collision path for different keys. Formula: offset = (key / listsize) adress = ((offset + old address) modulo listsize) + 1

For example if the key is 166702 and the listsize is 307, using the modulo division… offset = (166702 / 307) = 543 address = ((543 + 002) modulo 307) + 1 = 239

379452 Elmer

070918 Redjie

121267 Markh

378845 Hubert

160252 Arno

045128 Rollyn

[001]

[006]

[005]

[004]

[003]

[002]

[007]

[306][307]

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166702 Reymund

572556 Angelus

                                                      

  Hash collision resolved by linear probing (interval=1).