Pattern Matching for Separable Permutations

  title={Pattern Matching for Separable Permutations},
  author={Both Emerite Neou and Romeo Rizzi and St{\'e}phane Vialette},
Given a permutation \(\pi \) (called the text) of size n and another permutation \(\sigma \) (called the pattern) of size k, the NP-complete permutation pattern matching problem asks whether \(\sigma \) occurs in \(\pi \) as an order-isomorphic subsequence. In this paper, we focus on separable permutations (those permutations that avoid both 2413 and 3142, or, equivalently, that admit a separating tree). The main contributions presented in this paper are as follows. 

Pattern Matching for k-Track Permutations

This paper proposes and implements an exact algorithm, FPT for parameters k and \(|\pi |\), which allows to solve efficiently some large instances of the permutation pattern (PP) problem.

Permutation Pattern matching in (213, 231)-avoiding permutations

This work gives a linear-time algorithm in case both π and σ avoid the two size-3 permutations 213 and 231, and extends the research to bivincular patterns that avoid213 and 231 and presents a O(kn 4)-time algorithm.

The Complexity of Pattern Matching for 321-Avoiding and Skew-Merged Permutations

Two polynomial time algorithms for special cases of the Permutation Pattern Matching problem are presented, applicable if both $\pi$ and $\tau$ are $321$-avoiding and skew-merged.

Permutation Pattern Matching for Doubly Partially Ordered Patterns

The Doubly Partially Ordered Pattern Matching (or DPOP Matching) problem is studied, a natural extension of the Permutation pattern matching problem, and restrictions on several parameters/properties of the input are considered, giving a(n almost) complete landscape for the algorithmic complexity of the problem.

Unshuffling Permutations: Trivial Bijections and Compositions

The f-Unshuffle-Permutation problem is obtained, which is to decide whether there exists a permutation \(\sigma \in S_n\) such that Open image in new window .

Permutation pattern matching

Cette these s'interesse au probleme de la recherche de motif dans les permutations, qui a pour objectif de savoir si un motif apparait dans un texte, en prenant en compte que le motif et le texte

Theory and Applications of Models of Computation

  • P. Arno
  • Engineering
    Lecture Notes in Computer Science
  • 2019
This paper looks at ways of scheduling workloads over the multiplexed batteries to maximize the overall efficiency and considers two ways to model the efficiency and give efficient solutions to the same.



Longest Common Separable Pattern between Permutations

It is shown that the NP-hard problem of finding the longest common pattern between two permutations cannot be approximated better than within a ratio of $sqrt{Opt}$ (where $Opt$ is the size of an optimal solution) when taking common patterns belonging to pattern-avoiding classes of permutations.

Longest Common Separable Pattern Among Permutations

It is shown that the NP-hard problem of finding the longest common pattern between two permutations cannot be approximated better than within a ratio of √opt (where opt is the size of an optimal solution) when taking common patterns belonging to patternavoiding permutation classes.

Finding Pattern Matchings for Permutations

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).

A Fast Algorithm for Permutation Pattern Matching Based on Alternating Runs

This paper presents a fixed-parameter algorithm solving the NP-complete Permutation Pattern Matching problem with a worst-case runtime of 1.79, and proves that under standard complexity theoretic assumptions such a Fixedparameter tractability result is not possible for P.

The longest common pattern problem for two permutations

In this paper, we give a polynomial (O(n 8 )) algorithm for finding a longest common pattern between two permutations of size n given that one is separable. We also give an algorithm for general

Finding small patterns in permutations in linear time

A novel type of decompositions for permutations and a corresponding width measure is introduced and shown how to solve the Permutation Pattern problem in linear time if a bounded-width decomposition is given in the input.

Unshuffling Permutations

By using a pattern avoidance criterion on oriented perfect matchings, it is proved that recognizing square permutations is NP-complete.

Algorithms for Pattern Involvement in Permutations

By using carefully chosen data structures to fine tune the methods, it is established that any pattern of length 4 can be detected in O(n log n) time.

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.