1. Yalin Zhang zhangyl@tamu.edu

2. Huffman Coding

4. Variations of Huffman Coding Length-limited coding Unequal-cost coding Mixed-radix coding Reserved-length coding One-ended coding

5. Variations of Huffman Coding Standard binary treeMix-radix tree Reserved-length tree General approach: Dynamic Programming to build an optimal coding tree.

6. Top-Down DP for GMR coding Generalized-Mixed-Radix problem Both the arity of an internal node and the length of an edge depends on its level. Given a sequence of arities R = (r1, r2,...) and a sequence of edge lengths C = (c1, c2...), a generalized mixed radix (GMR) tree T satisfying R, C is a tree in which internal node v at level i − 1 has at most ri children and and the length of an edge from v to any of its children is ci

7. Top-Down DP for GMR coding

8. Top-Down Dynamic Program

9. Build optimal trees top-down, starting with a root; Expand tree level-by-level by making some nodes on the bottom level internal. Until a tree whose bottom level contains no internal nodes.

10. Top-Down Dynamic Program

14. Batching for Speed up

17. Results