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={International Symposium on Algorithms and Computation},
  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… 

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