ZeePedia Add to Favourites   |   Contact us


Database Management Systems

<<< Previous Hashing, Hash Functions, Hashed Access Characteristics, Mapping functions, Open addressing Next >>>
 
img
Database Management System (CS403)
VU
Lecture No. 36
Reading Material
"Database Management Systems", 2nd edition, Raghu Ramakrishnan, Johannes
Gehrke, McGraw-Hill
Database Management, Jeffery A Hoffer
Overview of Lecture
o Hashing
o Hashing Algorithm
o Collision Handling
In the previous lecture we have discussed file organization and techniques of file
handling. In today's lecture we will study hashing techniques, its algorithms and
collision handling.
Hashing
A hash function is computed on some attribute of each record. The result of the
function specifies in which block of the file the record should be placed .Hashing
provides rapid, non-sequential, direct access to records. A key record field is used to
calculate the record address by subjecting it to some calculation; a process called
hashing. For numeric ascending order a sequential key record fields this might
involve simply using relative address indexes from a base storage address to access
records. Most of the time, key field does not have the values in sequence that can
directly be used as relative record number. It has to be transformed. Hashing involves
computing the address of a data item by computing a function on the search key value.
A hash function h is a function from the set of all search key values K to the set of all
bucket addresses B.
265
img
Database Management System (CS403)
VU
·
We choose a number of buckets to correspond to the number of search key
values we will have stored in the database.
·
To perform a lookup on a search key value
, we compute
, and
search the bucket with that address.
·
If two search keys i and j map to the same address, because
, then the bucket at the address obtained will contain
records with both search key values.
·
In this case we will have to check the search key value of every record in
the bucket to get the ones we want.
·
Insertion and deletion are simple.
Hash Functions
A good hash function gives an average-case lookup that is a small constant,
independent of the number of search keys. We hope records are distributed uniformly
among the buckets. The worst hash function maps all keys to the same bucket. The
best hash function maps all keys to distinct addresses. Ideally, distribution of keys to
addresses is uniform and random.
Hashed Access Characteristics
Following are the major characteristics:
·
No indexes to search or maintain
·
Very fast direct access
·
Inefficient sequential access
·
Use when direct access is needed, but sequential access is not.
Mapping functions
The direct address approach requires that the function, h(k), is a one-to-one mapping
from each k to integers in (1,m). Such a function is known as a perfect hashing
function: it maps each key to a distinct integer within some manageable range and
enables us to trivially build an O(1) search time table.
Unfortunately, finding a perfect hashing function is not always possible. Let's say that
we can find a hash function, h(k), which maps most of the keys onto unique integers,
but maps a small number of keys on to the same integer. If the number of collisions
266
img
Database Management System (CS403)
VU
(cases where multiple keys map onto the same integer), is sufficiently small, then
hash tables work quite well and give O(1) search times.
Handling the Collisions
In the small number of cases, where multiple keys map to the same integer, then elements with
different keys may be stored in the same "slot" of the hash table. It is clear that when the hash function
is used to locate a potential match, it will be necessary to compare the key of that element with the
search key. But there may be more than one element, which should be stored in a single slot of the table.
Various techniques are used to manage this problem:
·
Chaining,
·
Overflow areas,
·
Re-hashing,
·
Using neighboring slots (linear probing),
·
Quadratic probing,
·
Random probing, ...
Chaining:
One simple scheme is to chain all collisions in lists attached to the appropriate slot.
This allows an unlimited number of collisions to be handled and doesn't require a
priori knowledge of how many elements are contained in the collection. The tradeoff
is the same as with linked lists versus array implementations of collections: linked list
overhead in space and, to a lesser extent, in time.
Re-hashing:
Re-hashing schemes use a second hashing operation when there is a collision. If
there is a further collision, we re-hash until an empty "slot" in the table is found.
The re-hashing function can either be a new function or a re-application of the
original one. As long as the functions are applied to a key in the same order, then
a sought key can always be located.
Linear probing:
One of the simplest re-hashing functions is +1 (or -1), ie on a collision; look in the
neighboring slot in the table. It calculates the new address extremely quickly and may
be extremely efficient on a modern RISC processor due to efficient cache utilization.
The animation gives you a practical demonstration of the effect of linear probing: it
also implements a quadratic re-hash function so that you can compare the difference.
267
img
Database Management System (CS403)
VU
h(j)=h(k), so the next hash function, h1 is used. A second collision occurs, so h2 is used.
Clustering:
Linear probing is subject to a clustering phenomenon. Re-hashes from one location occupy a block of
slots in the table which "grows" towards slots to which other keys hash. This exacerbates the collision
problem and the number of re-hashed can become large.
Overflow area:
Another scheme will divide the pre-allocated table into two sections: the primary area to which keys
are mapped and an area for collisions, normally termed the overflow area.
When a collision occurs, a slot in the overflow area is used for the new element and a
link from the primary slot established as in a chained system. This is essentially the
same as chaining, except that the overflow area is pre-allocated and thus possibly
faster to access. As with re-hashing, the maximum number of elements must be
known in advance, but in this case, two parameters must be estimated: the optimum
size of the primary and overflow areas.
268
img
Database Management System (CS403)
VU
Of course, it is possible to design systems with multiple overflow tables, or with a
mechanism for handling overflow out of the overflow area, which provide
flexibility without losing the advantages of the overflow scheme.
Collision handling
A well-chosen hash function can avoid anomalies which are result of an excessive
number of collisions, but does not eliminate collisions. We need some method for
handling collisions when they occur. We'll consider the following techniques:
·
Open addressing
·
Chaining
Open addressing:
The hash table is an array of (key, value) pairs. The basic idea is that when a (key,
value) pair is inserted into the array, and a collision occurs, the entry is simply
inserted at an alternative location in the array. Linear probing, double hashing, and
rehashing are all different ways of choosing an alternative location. The simplest
probing method is called linear probing. In linear probing, the probe sequence is
simply the sequence of consecutive locations, beginning with the hash value of the
key. If the end of the table is reached, the probe sequence wraps around and
continues at location 0. Only if the table is completely full will the search fail.
Summary Hash Table Organization:
Organization Advantages
Disadvantages
Unlimited number of elements
Overhead of multiple linked
Chaining
Unlimited number of collisions
lists
Re-hashing
Maximum
number
of
Fast re-hashing
elements must be known
Fast
access
through
use
of main table space
Multiple
collisions
may
become probable
Overflow
Fast access
Two
parameters
which
area
Collisions don't use primary table
govern
performance
space
need to be estimated
269
Table of Contents:
  1. Introduction to Databases and Traditional File Processing Systems
  2. Advantages, Cost, Importance, Levels, Users of Database Systems
  3. Database Architecture: Level, Schema, Model, Conceptual or Logical View:
  4. Internal or Physical View of Schema, Data Independence, Funct ions of DBMS
  5. Database Development Process, Tools, Data Flow Diagrams, Types of DFD
  6. Data Flow Diagram, Data Dictionary, Database Design, Data Model
  7. Entity-Relationship Data Model, Classification of entity types, Attributes
  8. Attributes, The Keys
  9. Relationships:Types of Relationships in databases
  10. Dependencies, Enhancements in E-R Data Model. Super-type and Subtypes
  11. Inheritance Is, Super types and Subtypes, Constraints, Completeness Constraint, Disjointness Constraint, Subtype Discriminator
  12. Steps in the Study of system
  13. Conceptual, Logical Database Design, Relationships and Cardinalities in between Entities
  14. Relational Data Model, Mathematical Relations, Database Relations
  15. Database and Math Relations, Degree of a Relation
  16. Mapping Relationships, Binary, Unary Relationship, Data Manipulation Languages, Relational Algebra
  17. The Project Operator
  18. Types of Joins: Theta Join, Equi–Join, Natural Join, Outer Join, Semi Join
  19. Functional Dependency, Inference Rules, Normal Forms
  20. Second, Third Normal Form, Boyce - Codd Normal Form, Higher Normal Forms
  21. Normalization Summary, Example, Physical Database Design
  22. Physical Database Design: DESIGNING FIELDS, CODING AND COMPRESSION TECHNIQUES
  23. Physical Record and De-normalization, Partitioning
  24. Vertical Partitioning, Replication, MS SQL Server
  25. Rules of SQL Format, Data Types in SQL Server
  26. Categories of SQL Commands,
  27. Alter Table Statement
  28. Select Statement, Attribute Allias
  29. Data Manipulation Language
  30. ORDER BY Clause, Functions in SQL, GROUP BY Clause, HAVING Clause, Cartesian Product
  31. Inner Join, Outer Join, Semi Join, Self Join, Subquery,
  32. Application Programs, User Interface, Forms, Tips for User Friendly Interface
  33. Designing Input Form, Arranging Form, Adding Command Buttons
  34. Data Storage Concepts, Physical Storage Media, Memory Hierarchy
  35. File Organizations: Hashing Algorithm, Collision Handling
  36. Hashing, Hash Functions, Hashed Access Characteristics, Mapping functions, Open addressing
  37. Index Classification
  38. Ordered, Dense, Sparse, Multi-Level Indices, Clustered, Non-clustered Indexes
  39. Views, Data Independence, Security, Vertical and Horizontal Subset of a Table
  40. Materialized View, Simple Views, Complex View, Dynamic Views
  41. Updating Multiple Tables, Transaction Management
  42. Transactions and Schedules, Concurrent Execution, Serializability, Lock-Based Concurrency Control, Deadlocks
  43. Incremental Log with Deferred, Immediate Updates, Concurrency Control
  44. Serial Execution, Serializability, Locking, Inconsistent Analysis
  45. Locking Idea, DeadLock Handling, Deadlock Resolution, Timestamping rules