A data processing apparatus has a compressor and an output interface. The compressor generates an output display data according to an input display data. The output interface packs the output display data into an output bitstream, and outputs the output bitstream to another data processing apparatus via a display interface. The display interface is a display serial interface (DSI) standardized by a Mobile Industry Processor Interface (MIPI) or an embedded display port (eDP) standardized by a Video Electronics Standards Association (VESA). In addition, the compressor adaptively adjusts a compression algorithm according to context characteristics in the input display data, power supply status, operational status of a storage device, image capture characteristic, configuration of the another data processing apparatus, and/or compression algorithm supported by the another data processing apparatus. Further, the another data processing apparatus adaptively adjusts a de-compression algorithm according to a compression algorithm supported by the compressor.