Abstract
Let a seed, S, be a string from the alphabet {1,*}, of arbitrary length k, which starts and ends with a 1. For example, S = 11*1. S occurs in a binary string T at position h if the length k substring of T ending at position h contains a 1 in every position where there is a 1 in S. We say that the 1s at the corresponding positions in T are covered. We are interested in calculating the probability distribution for the number of 1s covered by a seed S in an iid Bernoulli string of length n with probability of 1 equal to p. We refer to this new probability distribution as C nSp , for covered, with S being the seed. We present an efficient method to calculate this distribution exactly. Covered 1s represent matching positions detected in DNA sequences when using multiple hits of a spaced seed. Knowledge of the distribution provides a statistical threshold for distinguishing true homologies from randomly matching sequences.
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Benson, G., Mak, D.Y.F. (2008). Exact Distribution of a Spaced Seed Statistic for DNA Homology Detection. In: Amir, A., Turpin, A., Moffat, A. (eds) String Processing and Information Retrieval. SPIRE 2008. Lecture Notes in Computer Science, vol 5280. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-89097-3_27
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DOI: https://doi.org/10.1007/978-3-540-89097-3_27
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