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An Algorithm for Estimating all Matches Between Two Strings

Abstract : We give a randomized algorithm for estimating the score vector of matches between a text string of length~$N$ and a pattern string of length~$M$; this is the vector obtained when the pattern is slid along the text, and the number of matches is counted for each position. The randomized algorithm takes deterministic time $O( (N / M ) {\textstyle {\it Conv}} (M) )$ where ${\textstyle {\it Conv}} (M)$ is the time for performing a convolution of two vectors of size $M$ each. The algorithm finds an unbiased estimator of the scores, whose variance is particularly small for scores that are close to $M$, i.e., for approximate occurrences of the pattern in the text. No assumptions are made about the probabilistic characteristics of the input, or about the number of different symbols appearing in $T$ or $P$ (i.e., the alphabet size need not be much smaller than $M$). The solution extends to the weighted case and to higher dimensions.
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https://hal.inria.fr/inria-00073495
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Submitted on : Wednesday, May 24, 2006 - 1:02:47 PM
Last modification on : Friday, February 4, 2022 - 3:10:20 AM
Long-term archiving on: : Thursday, March 24, 2011 - 12:52:01 PM

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  • HAL Id : inria-00073495, version 1

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Mikhail J. Atallah, Frédéric Chyzak, Philippe Dumas. An Algorithm for Estimating all Matches Between Two Strings. [Research Report] RR-3194, INRIA. 1997. ⟨inria-00073495⟩

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