Yalin Zhang Huffman Coding Variations of Huffman Coding Length-limited coding Unequal-cost coding Mixed-radix coding Reserved-length.

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Presentation transcript:

Yalin Zhang

Huffman Coding

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

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

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

Top-Down DP for GMR coding

Top-Down Dynamic Program

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.

Top-Down Dynamic Program

Batching for Speed up

Results