The goal of this research is to study complexity issues, develop algorithms, and perform experiments with adaptive data compression algorithms, both lossless and lossy. We build upon our previous research and continue a blend of theoretical and experimental work. We are interested in methods that both compress well and can be implemented to run in real-time in high bandwidth applications where robustness with respect to channel errors / storage corruption may be required. General areas of research addressed are error resilience, 2D lossless compression, adaptive methods for (lossy) image and video compression, parallel algorithms and architectures, and automated browsing based upon the "learning" employed by adaptive compression methods.