1. Algorithm Design & Analysis – CS632 Group Project Group Members Bijay Nepal James Hansen-Quartey Winter 2002@UNH

2. INTRODUCTION  A Data compression technique  Developed by David Huffman, former professor of MIT, in 1952  A statistical method of compression  Analyses the input before compression

3. Types of Huffman Algorithm  Static Huffman  Adaptive Huffman: dynamically changes the code words according to probabilities of the symbols.  Extended Huffman: can encode groups of symbols rather than single symbols.

4. Encoding Steps in Huffman encoding  Compute the frequency of each characters or symbols  Sort them according to the frequency  Build the Huffman tree Build the Huffman tree  Transverse tree from root to leaf & assign 0 for left node path and 1 for right node path.  This gives the code word.

5. Building Huffman Tree 20100503043 7 27 57 abtksSP

6. Building Huffman Tree 10050203043 7 27 57 107

7. Building Huffman Tree 100 50203043 7 27 57 107 207 0 1 1 0 0 0 0 1 1 1 tSPsabk

8. Building Huffman Tree 10050203043 7 27 57 107 207 0 1 1 0 0 0 0 1 1 1 tSPsabk 0 10 11000 11001 1101 111 SP t b a s k Code word

9. Characteristics of Huffman codes  No code for a character is the prefix of the code for any other character  Huffman coding results in shorter average length of compressed (encoded) message  Most frequent characters are assigned to short code words.  Characters or symbols are always stored in leaves of Huffman tree.  Huffman coding works better when large variation in frequency of letters

10. Decoding  Read frequency from frequency table  Read encoded characters or symbols.  Build the tree and transverse according to the binary codeword.  Leaf value is the decoded symbol.

11. Algorithm for building tree C  Set of n characters and each character is defined with frequency f[c] Q  A priority queue Q, keyed on f Huffman ( C ) Q  C For I  1 to n – 1 Do Z  ALLCATE-NODE() X  LEFT[Z]  EXTRACT_MIN(Q) Y  RIGHT[Z]  EXTRACT_MIN(Q) f[Z]  f[X]+f[Y] INSERT(Q, Z) RETURN EXTRACT_MIN ( Q )

12. Time-complexity analysis  Q is implemented as heap. Therefore, for a set C of n characters, this can be done in O(n) time.  ‘for’ loop in the algorithm is executed exactly n-1 times and each heap operation requires O(log n) time.  Therefore, total running time is O(n log n)

13. Implementation Issues  Data structures Data structures  Sorting  Building tree  Encoding  Decoding

14. Drawbacks  This compression algorithm is mainly efficient in compressing text or program files.  Static Huffman is not suitable for image compression.  For small file, overhead is significant and hence less compression ratio.  Not suitable for live data compression as prior data analysis is not available.  Scans input data twice.

15. Application  Huffman compression is used in programs like pkZIP, gz, zoo and arj.  It is also used within JPEG and MPEG compression.

16. Thank You.