1. Huffman Coding with Non-Sorted Frequencies Shmuel Tomi Klein Dana Shapira Bar Ilan University, Ashkelon Academic College, ISRAEL

2. Outline Background and motivation Using non-sorted frequencies Relevance to other compression Conclusions Dynamic compression of data packets Background and motivation Using non-sorted frequencies Dynamic compression of data packets Relevance to other compression Conclusions

3. Sorted frequencies Sufficient but not necessary Huffman’s algorithm Construction in Code construction only

4. Applications Low text / code ratio Several codes Markov process encoding Dynamic coding schemes: Encoding based on

5. Optimal Trees 2 54 3 32 13 9 76 22 Huffman Tree 7 5 3 3 2 2 7 5 4 3 3 7 6 5 4 9 7 6 13 9 22

6. 2 55 3 23 1210 75 22 Optimal Trees 7 5 3 2 3 2 7 5 5 3 2 7 5 5 5 10 7 5 12 10 22 Non-Huffman Tree

7. 2 64 3 32 1210 75 22 Optimal Trees 7 5 3 3 2 2 7 5 4 3 3 7 5 6 4 10 7 5 12 10 22 Non-Huffman Tree

8. No restriction bad encoding 1 1 2 4 8 16 32 2n2n 1 1 2 4 8 16 2n2n

9. Restriction: order operations 7 5 3 3 2 2 2213 9 7 9 6 7 5 6 4 7 5 3 3 4

10. Start with any order Then use 2 queues Reversed order full tree

11. Partial Sort: parameter K W1W1 WKWK...W3W3 W2W2 Time: 4-grams3-grams2-grams1-gramsTests:21886602680852English 56078188642965131French

12. Average # bits/char vs # partition blocks English 2832128512 3 4 5 6 7 2048 1-grams 2-grams 3-grams 4-grams

13. French Average # bits/char vs # partition blocks 2832128512 3 4 5 6 7 2048 1-grams 2-grams 3-grams 4-grams

14. Dynamic compression of data packets Encoding based on

15. Bub- For-5 BubbleBlocked Block size Bigrams 5.065.063.812000 Comprs 5.065.063.8120000 11.67.330.12000 Time 15.211.137.420000 6.356.344.112000 Comprs 6.346.344.1120000 14.09.9286.22000 Time 17.613.4290.420000 French English

16. Relevance to other compression schemes Arithmetic coding 256-ary Huffman (s,c)-dense codes, Fibonacci codes Burrows-Wheeler Transform

17. Conclusion Not fully sorting the weights Time savings for sort intensive methods Compresion / Time tradeoff