Single and Multiple Consecutive Permutation Motif Search

  title={Single and Multiple Consecutive Permutation Motif Search},
  author={Djamal Belazzougui and Adeline Pierrot and Mathieu Raffinot and St{\'e}phane Vialette},
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… 

Shape-Preserving Pattern Matching

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

Order-Preserving Indexing (cid:73)

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.

Toward a Succinct Index for Order-Preserving Pattern Matching

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.

An Encoding for Order-Preserving Matching

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

The order-preserving model (op-model, in short) was introduced quite recently but has already attracted significant attention because of its applications in data analysis and algorithms to compute several types of periods in this setting are introduced.

Order-Preserving Pattern Matching Indeterminate Strings

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.

Efficient Algorithms for the Order Preserving Pattern Matching Problem

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.

A compact index for order‐preserving pattern matching

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

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.



Pattern Matching for Permutations

A polynomial time algorithm is given for the decision problem, and the corresponding counting problem, in the case that P is separable—i.e. contains neither the subpattern (3,1, 4,2) nor its reverse, the sub pattern (2,4, 1,3).

The Complexity of Pattern Matching for a Random String

  • A. Yao
  • Mathematics, Computer Science
    SIAM J. Comput.
  • 1979
It is proved that, for large m, almost all patterns $\alpha$ of length m satisfy c($\alpha), which confirms a conjecture raised in a recent paper by Knuth, Morris, and Pratt [1977].

On Complexity of the Subpattern Problem

It turns out that for most permutations $C^{\bf T}(\pi) = \Omega(k)$, and thus, in general, the upper bound on the running time cannot be significantly improved using this approach.

Average complexity of exact and approximate multiple string matching

Dynamic ordered sets with exponential search trees

We introduce exponential search trees as a novel technique for converting static polynomial space search structures for ordered sets into fully-dynamic linear space data structures. This leads to an

Patterns in Permutations and Words

  • S. Kitaev
  • Mathematics
    Monographs in Theoretical Computer Science. An EATCS Series
  • 2011
The author collects the main results in the field in this up-to-date, comprehensive reference volume and highlights significant achievements in the area, and points to research directions and open problems.

Deterministic sorting in O(nlog log n) time and linear space

A fast deterministic algorithm for integer sorting in linear space which sorts integers in the range of 0, 1, 2, &1dots;, <i>m</i>—1 inlinear space in time and linear space and uses randomization.

String Matching Algorithms and Automata

  • Imre Simon
  • Computer Science
    Results and Trends in Theoretical Computer Science
  • 1994
The structure of finite automata recognizing sets of the form A*p, for some word p, is studied, and the results obtained are used to improve the Knuth-Morris-Pratt string searching algorithm.

Preserving order in a forest in less than logarithmic time

  • P. Boas
  • Computer Science
    16th Annual Symposium on Foundations of Computer Science (sfcs 1975)
  • 1975