The context-tree weighting method is a universal data compression technique for binary tree sources that performs a "double mixture." It efficiently weights coding distributions for all bounded memory tree sources, achieving a desirable distribution for unknown models and parameters. The method has linear computational and storage complexity in the source sequence length. The paper derives an upper bound on the cumulative redundancy, which includes coding, parameter, and model redundancy. This bound holds for all sequence lengths, not just asymptotically large ones. The analysis is based on standard techniques and is extremely simple. The method is optimal, achieving the Rissanen lower bound on redundancy. The method uses a context tree to estimate the state of the tree source and generate the next symbol. It avoids specifying artificial parameters that affect performance for finite sequences. Instead, it uses model weighting techniques, which perform well both on average and for individual sequences. The method is based on tree-recursive model weighting, resulting in a simple and effective coding method. The paper defines binary bounded memory tree sources and their properties. It discusses the use of context trees for modeling and coding, and introduces the concept of a weighted context tree. The method is shown to be optimal in terms of redundancy, achieving the Rissanen lower bound. The paper also discusses the implementation of the context-tree weighting method, including encoding and decoding processes, and analyzes its computational complexity. The method is shown to be effective for both finite and infinite memory tree sources. It is also applicable to non-binary sources, with straightforward generalizations. The paper concludes that the context-tree weighting method is a powerful and efficient approach to universal data compression for tree sources.The context-tree weighting method is a universal data compression technique for binary tree sources that performs a "double mixture." It efficiently weights coding distributions for all bounded memory tree sources, achieving a desirable distribution for unknown models and parameters. The method has linear computational and storage complexity in the source sequence length. The paper derives an upper bound on the cumulative redundancy, which includes coding, parameter, and model redundancy. This bound holds for all sequence lengths, not just asymptotically large ones. The analysis is based on standard techniques and is extremely simple. The method is optimal, achieving the Rissanen lower bound on redundancy. The method uses a context tree to estimate the state of the tree source and generate the next symbol. It avoids specifying artificial parameters that affect performance for finite sequences. Instead, it uses model weighting techniques, which perform well both on average and for individual sequences. The method is based on tree-recursive model weighting, resulting in a simple and effective coding method. The paper defines binary bounded memory tree sources and their properties. It discusses the use of context trees for modeling and coding, and introduces the concept of a weighted context tree. The method is shown to be optimal in terms of redundancy, achieving the Rissanen lower bound. The paper also discusses the implementation of the context-tree weighting method, including encoding and decoding processes, and analyzes its computational complexity. The method is shown to be effective for both finite and infinite memory tree sources. It is also applicable to non-binary sources, with straightforward generalizations. The paper concludes that the context-tree weighting method is a powerful and efficient approach to universal data compression for tree sources.