Approximate string searching with fast fourier transforms and simplexes

Previous algorithms for solving the approximate string matching with Hamming distance problem with wildcard ("don't care") characters have been shown to take \(O(|\Sigma| N \log M)\) time, where \(N\) is the length of the text, \(M\) is the length of the pattern, and \(|\Sigma|\) is the size of the alphabet. They make use of the Fast Fourier Transform for efficiently calculating convolutions. We describe a novel approach of the problem, which makes use of special encoding schemes that depend on \((|\Sigma| - 1)\)-simplexes in \((|\Sigma| - 1)\)-dimensional space.