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- W2103156536 abstract "Let t be a permutation (that shall play the role of the text) on [n] and a motif p be a sequence of m distinct integer(s) of [n], m ≤ n. The motif p occurs in t in position i if and only if p 1 …p m is order-isomorphic to t i …t i + m − 1, that is, for all 1 ≤ k < ℓ ≤ m, p k > p ℓ if and only if t i + k − 1 > t i + ℓ − 1. Searching for a motif p in a text t consists in identifying all occurrences of p in t. We first present a forward automaton which allows us to search for p in t in O(m 2loglogm + n) time. We then introduce a Morris-Pratt automaton representation of the forward automaton which allows us to reduce this complexity to O(mloglogm + n) at the price of an additional amortized constant term. The latter automaton occupies O(m) space. We then extend the problem to search for a set of motifs and exhibit a specific Aho-Corasick like algorithm. Next we present a sub-linear average case search algorithm running in $Oleft(frac{mlog m}{loglog m}+frac{nlog m}{mloglog m}right)$ time, that we eventually prove to be optimal on average." @default.
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- W2103156536 date "2013-01-01" @default.
- W2103156536 modified "2023-10-12" @default.
- W2103156536 title "Single and Multiple Consecutive Permutation Motif Search" @default.
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- W2103156536 doi "https://doi.org/10.1007/978-3-642-45030-3_7" @default.
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