Approximating text-to-pattern distance via dimensionality reduction
P Uznański - arXiv preprint arXiv:2002.03459, 2020 - arxiv.org
arXiv preprint arXiv:2002.03459, 2020•arxiv.org
Text-to-pattern distance is a fundamental problem in string matching, where given a pattern
of length $ m $ and a text of length $ n $, over an integer alphabet, we are asked to compute
the distance between pattern and the text at every location. The distance function can be eg
Hamming distance or $\ell_p $ distance for some parameter $ p> 0$. Almost all state-of-the-
art exact and approximate algorithms developed in the past $\sim 40$ years were using FFT
as a black-box. In this work we present $\widetilde {O}(n/\varepsilon^ 2) $ time algorithms for …
of length $ m $ and a text of length $ n $, over an integer alphabet, we are asked to compute
the distance between pattern and the text at every location. The distance function can be eg
Hamming distance or $\ell_p $ distance for some parameter $ p> 0$. Almost all state-of-the-
art exact and approximate algorithms developed in the past $\sim 40$ years were using FFT
as a black-box. In this work we present $\widetilde {O}(n/\varepsilon^ 2) $ time algorithms for …
Text-to-pattern distance is a fundamental problem in string matching, where given a pattern of length and a text of length , over an integer alphabet, we are asked to compute the distance between pattern and the text at every location. The distance function can be e.g. Hamming distance or distance for some parameter . Almost all state-of-the-art exact and approximate algorithms developed in the past years were using FFT as a black-box. In this work we present time algorithms for -approximation of distances, and algorithm for approximation of Hamming and distances, all without use of FFT. This is independent to the very recent development by Chan et al. [STOC 2020], where algorithm for Hamming distances not using FFT was presented -- although their algorithm is much more "combinatorial", our techniques apply to other norms than Hamming.
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