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Query Processing and Optimization, Study notes of Distributed Database Management Systems

Assam University Distributed Database Management Systems

Translating SQL queries into relational algebra, Basic algorithms - Sorting: internal sorting and external sorting - Implementing the SELECT operation - Implementing the JOIN operation - Implementing the Project operation - Other operations • Heuristics for query optimization, What is a heap? • MaxHeap and Maintenance of MaxHeaps - MaxHeapify - BuildMaxHeap • Heapsort - Algorithm - Heapsort analysis

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Sept. 2023 Dr. Yangjun Chen ACS-4902 1

Query Processing and Optimization

(Ch. 18, 3rd –Ch. 15, 4th ed. 5th ed., Ch. 19, 6th

ed., Ch. 18, 19, 7th ed.)

•Processing a high-level query

•Translating SQL queries into relational algebra

•Basic algorithms

- Sorting: internal sorting and external sorting

- Implementing the SELECT operation

- Implementing the JOIN operation

- Implementing the Project operation

- Other operations

•Heuristics for query optimization

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Query Processing and Optimization

(Ch. 18, 3

- Ch. 15, 4

th ed. 5

th ed., Ch. 19, 6

ed., Ch. 18, 19, 7

th ed.)

Processing a high-level query
Translating SQL queries into relational algebra
Basic algorithms
- Sorting: internal sorting and external sorting
- Implementing the SELECT operation
- Implementing the JOIN operation
- Implementing the Project operation
- Other operations
Heuristics for query optimization

Steps of processing a high-level query

Scanning, Parsing, Validating

Query in a high-level language

Intermediate form of query

Query optimization

Execution plan

Query code generation

Code to execute the query

Runtime database processor

Result of query

SELECT MAX(SALARY)

FROM EMPLOYEE

WHERE DNO = 5

SELECT LNAME, FNAME

FROM EMPLOYEE

WHERE SALARY > c

F

MAX SALARY

DNO=

(EMPLOYEE))

LNAME FNAME

SALARY>C

(EMPLOYEE))

Translating SQL queries into relational algebra
- translate query blocks into relational algebra expressions

Basic algorithms
- sorting: internal sorting and external sorting
- algorithm for SELECT operation
- algorithm for JOIN operation
- algorithm for PROJECT operation
- algorithm for SET operations
- implementing AGGREGATE operation
- implementing OUTER JOIN

Basic algorithms
- different internal sorting methods:

sorting numbers

Input n numbers. Sort them such that the numbers are

ordered increasingly.

3 9 1 6 5 4 8 2 10 7

1 2 3 4 5 9 7 8 9 10

main idea:

1st step: 3 9 1 6 5 4 8 2 10 7

2nd step: 1 9 3 6 5 4 8 2 10 7

1 2 3 6 5 4 8 9 10 7

… ...

swap

Basic algorithms
- A simple sorting algorithm

Heapsort

What is a heap?
MaxHeap and Maintenance of MaxHeaps
- MaxHeapify
- BuildMaxHeap
Heapsort
- Algorithm
- Heapsort analysis

Heapsort

Combines the better attributes of merge sort and

insertion sort.

Like merge sort, but unlike insertion sort, running time

is O ( n lg n ).

Like insertion sort, but unlike merge sort, sorts in

place.

Introduces an algorithm design technique
- Create data structure ( heap ) to manage information

during the execution of an algorithm.

The heap has other applications beside sorting.
- Priority Queues

Data Structure Binary Heap

length[ A ] – number of elements in array A.
heap-size[ A ] – number of elements in heap stored in A.
- heap-size[ A ]  length[ A ]

(^2 )

4 5 6 7

(^8 9 )

1 2 3 4 5 6 7 8 9 10

Searching the tree in breadth-first

fashion, we will get the array.

Last row filled from left to right.

Heap Property (Max and Min)

Max-Heap
- For every node excluding the root, the value stored in

that node is at most that of its parent: A [ parent [ i ]]  A [ i ]

Largest element is stored at the root.
In any subtree, no values are larger than the value

stored at the subtree’s root.

Min-Heap
- For every node excluding the root, the value stored in

that node is at least that of its parent: A [ parent [ i ]]  A[ i ]

Smallest element is stored at the root.
In any subtree, no values are smaller than the value

stored at the subtree’s root

1 2 3 4 5 6 7 8 9 10

(^2 )

4 5 6 7

(^8 9 )

exchange

Heaps in Sorting

Use max-heaps for sorting.
The array representation of a max-heap is not sorted.
Steps in sorting

(i) Convert the given array of size n to a max-heap ( BuildMaxHeap )

(ii) Swap the first and last elements of the array.

Now, the largest element is in the last position – where it

belongs.

That leaves n – 1 elements to be placed in their appropriate

locations.

However, the array of first n – 1 elements is no longer a max-

heap.

Float the element at the root down one of its subtrees so that

the array remains a max-heap ( MaxHeapify )

Repeat step (ii) until the array is sorted.

MaxHeapify

Suppose two subtrees are max-heaps,

but the root violates the max-heap

property.

Fix the offending node by exchanging the value at the node

with the larger of the values at its children.

May lead to the subtree at the child not being a max

heap.

Recursively fix the children until all of them satisfy the max-

heap property.

MaxHeapify – Example

MaxHeapify( A , 2)

2 3

4 5 6 7

9 10

Query Processing and Optimization, Study notes of Distributed Database Management Systems

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Query Processing and Optimization

F

(EMPLOYEE))

(EMPLOYEE))

Heapsort