This paper presents a novel approach for parallel sorting on stream processing architectures. It is based on adaptive bitonic sorting. For sorting n values utilizing p stream processor units, this approach achieves the optimal time complexity O((n log n)/p). This approach is competitive with common sequential sorting algorithms not only from a theoretical viewpoint, it is also very fast from a practical viewpoint. The paper presents an implementation on modern programmable graphics hardware (GPUs). On recent GPUs this optimal parallel sorting approach has shown to be remarkably faster than sequential sorting on the CPU, and it is also faster than previous non-optimal sorting approaches on the GPU for sufficiently large input sequences. (GPU-ABiSort: Optimal Parallel Sorting on Stream Architectures Alexander Gress and Gabriel Zachmann. Proc. 20th IEEE Int'l Parallel and Distributed Processing Symposium (IPDPS), 2006.)