Accelerating the LZ-complexity algorithm

The Lempel Ziv complexity of a string has recently been used in pattern recognition and classification as part of a string distance function. Its main advantage is that it can measure dissimilarity between a pair of strings of different lengths. This is very useful for machine learning on unstructured data since such data is not restricted to a fixed input dimensionality. The standard computation of LZ-complexity is inherently serial and is not suitable for processing large unstructured data. Hence, we propose a parallel algorithm that computes the LZ-complexity of strings whose length is limited only by the amount of memory, typically in the tens of gigabytes. The algorithm is implemented in CUDA on a GPU. Its speed-up factor is approximately n^2/3 for strings of length n, for at least up to n = 2Mb. For instance, on 2Mb strings, the speed-up is 150. We compare the execution times of kernel variants with shared and global memory. The more efficient variant obtains approximately 90% GPU utilization.