Efficient Implementations of the Approximate String Matching on the Memory Machine Models

The Discrete Memory Machine (DMM) and the Unified Memory Machine (UMM) are theoretical parallel computing models that capture the essence of the shared memory access and the global memory access of GPUs. The approximate string matching for two strings X and Y is a task to find a sub string of Y most similar to X. The main contribution of this paper is to show efficient implementations of approximate string matching on the memory machine models. Our best implementation for strings X and Y with length m and n (m≤n), respectively, runs in O(mn/w + ml) time units using n threads both on the DMM on the UMM with width w and latency l.