Huffman Coding: Design, Analysis, and Implementation, Lecture notes of Design and Analysis of Algorithms

Download Huffman Coding: Design, Analysis, and Implementation and more Lecture notes Design and Analysis of Algorithms in PDF only on Docsity! BCSE204L Design and Analysis of Algorithms Module-1 Huffman Coding (Greedy Technique) Dr Athira K SCOPE Data Compression Requirements •Storage and communication •Huffman codes compress data very effectively: savings of 20% to 90% are typical •Greedy on the frequency of each character in the data •Huffman coding is used widely as the basic building block of numerous other compression algorithms •Fixed length and variable length coding Prefix Codes Example •Encoding:- 𝑎𝑏𝑐→ 0 · 101 · 100 where · is concatenation •Therefore, instead of 𝑎𝑏𝑐 we send 0101100 •Decoded at the receiving end without ambiguity, provided the receiver must know the coding table Huffman Coding •Produces optimal prefix codes based on the frequency of occurrence of characters within the message/data • Follows greedy strategy •Assume that 𝐶 is a set of 𝑛 characters and that each • character 𝑐 ∈ 𝐶 is an object with an attribute 𝑐. 𝑓𝑟𝑒𝑞 giving its frequency Huffman Tree •Algorithm builds Huffman tree, 𝑇 in a bottom up manner • Initially a set of |𝐶| leaves and performs |𝐶| − 1 merge operations •Uses a min-priority queue 𝑄, keyed on the 𝑓𝑟𝑒𝑞 attribute Exercise •Draw the Huffman tree and generate the Huffman code •Answer: a=111, e=10, i=00, o=11001, u=1101, s=01, t=11000 a e i o u s t 10 15 12 3 4 13 1 Thank you..