# Single and Multiple Consecutive Permutation Motif Search

@inproceedings{Belazzougui2013SingleAM, title={Single and Multiple Consecutive Permutation Motif Search}, author={Djamal Belazzougui and Adeline Pierrot and Mathieu Raffinot and St{\'e}phane Vialette}, booktitle={ISAAC}, year={2013} }

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 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…

## 22 Citations

### Shape-Preserving Pattern Matching

- Mathematics, Computer ScienceICTCS
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Two linear-time algorithms are presented which, given a text y and a pattern x over an integer alphabet, finds all the factors of y that are shape-isomorphic to x, and this problem is called shape-preserving pattern-matching problem.

### Order-Preserving Indexing (cid:73)

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An index is proposed that enables order-preserving pattern matching queries in time proportional to pattern length, and an O ( n (cid:112) log n )-time algorithm is given constructing complete order- Preserving su ﬃ x trees.

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This paper introduces the first index for this problem that uses sublinear space in addition to the data, which is useful when the authors want to search repeatedly in datasets to which they have read-only access and which are too large to copy conveniently.

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This paper gives the first encoding data structure for the challenging problem of order-preserving pattern matching, and shows how an O(n log log n)-bit encoding can be built such that later, given a pattern P[1..m] with m >= log^c n, it can return the number of orderserving occurrences of P in S in O(m) time.

### String Periods in the Order-Preserving Model

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### Order-Preserving Pattern Matching Indeterminate Strings

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This paper provides the first polynomial algorithms to answer the muOPPM problem when: 1) indetermination is observed on the pattern or text; and 2) ind determination is observation on both the pattern and the text and given by uncertainties between pairs of characters.

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This paper presents two new filtering approaches which turn out to be much more effective in practice than the previously presented methods by reducing the number of false positives up to 99 % and up to 2 times faster than the previous solutions.

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This work proposes a space‐efficient index that works well in practice despite its lack of good worst‐case time bounds, and is the first one offering simultaneously small space usage and fast retrieval.

### Algorithms for Order-Preserving Matching

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The OPM problem is to find all the substrings in the text which have the same length and relative order as the pattern, where the relative order is the numerical order of the numbers in a string.

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