# Lecture 4 Sorting Networks Comparator comparator A Sorting

- Slides: 42

Lecture 4 Sorting Networks

Comparator comparator

A Sorting Network 9 5 2 2 5 9 6 5 2 2 5 6 6 6 9 9 A sorting network is a comparison network which output monotone nondecreasing sequence for every input.

Depth 9 5 2 2 5 9 6 5 2 2 5 6 6 6 9 9 Depth is the maximum number of comparators on a path from an input wire to an output wire.

Depth = parallel time 9 5 2 2 5 9 6 5 2 2 5 6 6 6 9 9 Depth is the maximum number of comparators on a path from an input wire to an output wire.

Insertion Sort

key

Sorting network constructed from insertion sort.

How to construct a sorting network from merging sort?

Divide and Conquer • Divide the problem into subproblems. • Conquer the subproblems by solving them recursively. • Combine the solutions to subproblems into the solution for original problem.

Merge Sort

Procedure

Structure Sorting network Merging network Sorting network

Construction of Merging Network • 0 -1 principal. • Bitonic sorter. • Merging network.

0 -1 principal

Lemma

Proof of 0 -1 Principal

Bitonic Sequence

Bitonic 0 -1 Sequence

Some Properties

The half-cleaner bitonic 0 0 1 0 1 1 0 0 0 1 bitonic clean bitonic

The half-cleaner bitonic 0 0 1 1 1 0 1 bitonic clean

Lemma (a)One of two halfs is bitonic clean. (b) every number in the 1 st half ≤ any element in the 2 nd half.

Proof (case 1) 0 0 0 1 0 1 0

Proof (case 2) 0 0 1 0 0 0 1

Proof (case 3) 0 0 0 1 1 1 0 0 1

Proof (case 4) 0 0 0 1 1 0 0 0 1

Proof (case 5) 1 0 1 0 1 1 1

Proof (case 6) 1 1 0 1 0 1 1

Proof (case 7) 0 1 1 0 0 1 1

Proof (case 8) 0 1 1 0 1

bitonic sorted Half cleaners

sorted 0 0 0 1 0 0 0 sorted 0 1 1 1 0 1 1 Half cleaners Merging Network

Structure Sorting network Merging network Sorting network

Sorting Network Merging Networks

What we learnt in this lecture? • What is sorting network? • Depth = parallel time. • Sorting network from Merge sort.

Permutation Network • Switching network • Rearrangeability • Nework with 2 x 2 crossbars

Crossbar Switch A crossbar switch can realize any matching between Inputs and outputs.

3 -stage Clos Network 1 n n m

Rearrangeability Theorem

Network with 2 x 2 crossbars

Puzzle

- 4 bit comparator truth table and logic diagram
- What is internal and external sorting
- Sorting networks
- 01:640:244 lecture notes - lecture 15: plat, idah, farad
- Basestore iptv
- Datagram networks and virtual circuit networks
- Comparator instrument
- Binary subtractor
- Fungsi half adder
- Comparator
- N bit comparator
- Double bounded comparator
- Precision comparator
- Tesa gauge block comparator
- Applications of comparator
- Sahlis method
- Double bounded comparator
- Java comparator comparing boolean
- Ideal comparator
- Aci 224
- Sigma comparator
- Foster and freeman vsc 80 price
- Iterator
- Window comparator with hysteresis
- Op amp comparator circuit
- Disadvantages of optical profile projector
- Searching and sorting in java
- Non deterministic algorithm for sorting
- Harry poter houses
- Fluorescence activated cell sorting
- Changes in wave properties sorting activity answer key
- Topological ordering
- Internal sorting
- Inplace sort
- Fluorescence activated cell sorting
- Bernadus artinya
- Shapes objectives
- Simplest sorting algorithm
- Pseudocode adalah
- Introduction to sorting
- Pigeon hole algorithm
- Internal sorting example
- Tujuan melakukan sorting data di dokumen adalah