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A linear time algorithm for consecutive permutation pattern matching

M. Kubica, T. Kulczyński, J. Radoszewski, W. Rytter, T. Waleń
2013 Information Processing Letters  
A factor is a subsequence of consecutive symbols of y, so we call our problem the consecutive permutation pattern matching.  ...  We say that two sequences x and w of length m are order-isomorphic (of the We present a simple linear time algorithm for checking if a given sequence y of length n contains a factor which is order-isomorphic  ...  We present a linear time algorithm for permutation pattern matching of consecutive patterns.  ... 
doi:10.1016/j.ipl.2013.03.015 fatcat:yp5pzchhzzek5cd2m3zla6qhg4

Pattern matching in (213,231)-avoiding permutations [article]

Both Emerite Neou, Romeo Rizzi, Stéphane Vialette
2015 arXiv   pre-print
We give a linear-time algorithm in case both π and σ avoid the two size-3 permutations 213 and 231.  ...  For the special case where only σ avoids 213 and 231, we present a O(max(kn^2,n^2((n))) time algorithm.  ...  In Section 5 we give a polynomial-time algorithm for (213, 231)-avoiding bivincular patterns. In Section 6 we consider the problem of finding the longest (213, 231)-avoiding pattern in permutations.  ... 
arXiv:1511.01770v1 fatcat:5vsxmo5vszd4nd3lz2mb4k4vie

Testing for the consecutive ones property, interval graphs, and graph planarity using PQ-tree algorithms

Kellogg S. Booth, George S. Lueker
1976 Journal of computer and system sciences (Print)  
The consecutive ones test is extended to a test for interval graphs using a recently discovered fast recognition algorithm for chordal graphs.  ...  All of these algorithms require a number of steps linear in the size of their input.  ...  Ullman for their many helpful suggestions during both the research and presentation of these results.  ... 
doi:10.1016/s0022-0000(76)80045-1 fatcat:rvplpslsifa7hcvvc572m4ldy4

The computational landscape of permutation patterns [article]

Marie-Louise Bruner, Martin Lackner
2014 arXiv   pre-print
In this paper we draw a map of the computational landscape of permutation pattern matching with different types of patterns.  ...  Every type of permutation pattern naturally defines a corresponding computational problem: Given a pattern P and a permutation T (the text), is P contained in T?  ...  Acknowledgements We wish to thank HenningÚlfarsson for drawing our attention to marked mesh, decorated and other types of patterns, Sergey Kitaev for helping us with notational questions and the anonymous  ... 
arXiv:1301.0340v2 fatcat:of4huwt4dna2vd2gusyvpxpm5e

A Note on Scoring Clones Given a Probe Ordering

MUDITA JAIN, EUGENE W. MYERS
1995 Journal of Computational Biology  
The algorithm runs in time linear in the number of blocks of ones in the underlying sparse incidence matrix.  ...  Since the clones are intervals of the DNA strand, a permutation of the rows/probes that gives the permuted matrix ¥ the consecutive ones  ...  Acknowledgement The authors wish to thank one of the referees whose comments lead to a significantly simpler exposition of the sparse algorithm.  ... 
doi:10.1089/cmb.1995.2.33 pmid:7497118 fatcat:t2epcnnsonbf7pj4e4mzm7eagy

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

Both Neou, Romeo Rizzi, Stéphane Vialette
2017 Discrete Mathematics & Theoretical Computer Science  
We give a linear-time algorithm in case both π and σ avoid the two size-3 permutations 213 and 231.  ...  For the special case where only σ avoids 213 and 231, we present a O(max(kn 2 , n 2 log log n)-time algorithm.  ...  Section 3 is devoted to presenting an online linear-time algorithm in case both permutations are wedge permutations, whereas Section 4 focuses on the case where only the pattern is a wedge permutation.  ... 
doi:10.46298/dmtcs.1329 fatcat:wo7fipgr4zazbpxebdpinysk3a

Pattern Matching for Separable Permutations [chapter]

Both Emerite Neou, Romeo Rizzi, Stéphane Vialette
2016 Lecture Notes in Computer Science  
This improves upon the existing O(n 8 ) time algorithm. -Finally, we give a O(n 6 k) time and O(kn 4 ) space algorithm to detect an occurrence of a bivincular separable permutation in a permutation.  ...  -In case both the text and the pattern are separable permutations, we give a more practicable alternative O(n 2 k) time and O(nk) space algorithm.  ...  Since σ is a separable permutation, we can assume that we are given in addition a separating tree T σ for σ (constructing a separating tree of a separable permutation is linear time and space [5] ).  ... 
doi:10.1007/978-3-319-46049-9_25 fatcat:73qkwvhanjgobegpfqmxvfk3f4

Single and Multiple Consecutive Permutation Motif Search [chapter]

Djamal Belazzougui, Adeline Pierrot, Mathieu Raffinot, Stéphane Vialette
2013 Lecture Notes in Computer Science  
We then extend the problem to search for a set of patterns and exhibit a specific Aho-Corasick like algorithm.  ...  Next we present a sub-linear average case search algorithm running in O m log m log log m + n log m m log log m time, that we eventually prove to be optimal on average.  ...  Acknowledgements We would like to thanks Carine Pivoteau, Cyril Nicaud and Elie de Panafieu for checking parts of our calculus.  ... 
doi:10.1007/978-3-642-45030-3_7 fatcat:ih43vxy6ifdg7mu7jejz37odeu

Faster Exponential Algorithm for Permutation Pattern Matching [article]

Pawel Gawrychowski, Mateusz Rzepecki
2021 arXiv   pre-print
The Permutation Pattern Matching problem asks, given two permutations σ on n elements and π, whether σ admits a subsequence with the same relative order as π (or, in the counting version, how many such  ...  We design a simple and faster 𝒪(1.415^n) time algorithm for both the detection and the counting version. We also prove that this is optimal among a certain natural class of algorithms.  ...  The corresponding general algorithmic question called Permutation Pattern Matching (PPM) is to decide, for a given length-n permutation σ and length-k permutation π, if π σ.  ... 
arXiv:2108.11475v1 fatcat:qwmzto4s2vddxlfleq2ehfffr4

Sub-quadratic time and linear space data structures for permutation matching in binary strings

Tanaeem M. Moosa, M. Sohel Rahman
2012 Journal of Discrete Algorithms  
Given a pattern P of length n and a text T of length m, the permutation matching problem asks whether any permutation of P occurs in T .  ...  Indexing a string for permutation matching seems to be quite hard in spite of the existence of a simple non-indexed solution.  ...  Furthermore, Permutation Matching is a special case of approximate pattern matching and has been used as a filtering step in the approximate pattern matching algorithms [5] .  ... 
doi:10.1016/j.jda.2011.08.003 fatcat:aiy4c2t27zginovpxeccctlyra

Counting preimages of TCP reordering patterns

Anders Hansson, Gabriel Istrate
2008 Discrete Applied Mathematics  
A ∈ B −1 (W ) for some permutation A of {1, 2, . . . , n}), and a linear time algorithm that, given a valid buffer sequence W of length n, constructs a permutation A in the preimage of W . • We show that  ...  the problem of counting the number of permutations in B −1 (W ) has a polynomial time algorithm. • We also show how to extend these results to sequences of IDs that contain repeated packets.  ...  Department of Energy under contracts W-705-ENG-36 and DE-AC52-06NA25396, and by a Exploratory Research PN-II ''Idei'' grant from the Romanian Government.  ... 
doi:10.1016/j.dam.2008.05.011 fatcat:thzgcmfb5jfk3lfcmltujsii3q

PQR sort: using PQR trees for binary matrix reorganization

Celmar Guimarães da Silva, Marivaldo Felipe de Melo, Felipi de Paula e Silva, João Meidanis
2014 Journal of the Brazilian Computer Society  
Results: We found that PQR sort is an interesting method for minimizing minimal span loss functions based on Jaccard or simple matching coefficients, specially for a given pattern called Rectnoise with  ...  Matrix reordering algorithms, such as 2D sort and Sugiyama-based reordering, permute matrix rows and columns in order to highlight hidden patterns.  ...  Currently, there are only two algorithms to create PQR trees [16, 17] . The algorithm by Telles and Meidanis [16] is an almost linear time, incremental algorithm.  ... 
doi:10.1186/1678-4804-20-3 fatcat:qo4o23tpw5eihi6kabiv33s5cm

Minimising the number of gap-zeros in binary matrices

Konstantin Chakhlevitch, Celia A. Glass, Natalia V. Shakhlevich
2013 European Journal of Operational Research  
We study a problem of minimising the total number of zeros in the gaps between blocks of consecutive ones in the columns of a binary matrix by permuting its rows.  ...  One of the heuristics is particularly effective, especially for problems with a large number of rows.  ...  Thus Step 2.1 of algorithm ClassOpt can be implemented in O(n) time. Therefore finding the best matches for all m rows of matrix A incurs O(mn) time in Step 2.  ... 
doi:10.1016/j.ejor.2013.01.028 fatcat:e73sregpsnd43gtwwvp3ttci4a

Finding and counting permutations via CSPs [article]

Benjamin Aram Berendsohn, László Kozma, Dániel Marx
2019 arXiv   pre-print
Perhaps the most natural algorithmic question in this area is deciding whether a given permutation of length n contains a given pattern of length k.  ...  Our algorithms can also count, within the same running time, the number of occurrences of a pattern.  ...  An earlier version of the paper contained a mistake in the analysis of the algorithm for Theorem 2. We thank Günter Rote for pointing out the error.  ... 
arXiv:1908.04673v1 fatcat:uzraxyou3jdybawbiojy3l2gk4

Finding and Counting Permutations via CSPs

Benjamin Aram Berendsohn, László Kozma, Dániel Marx
2021 Algorithmica  
Perhaps the most natural algorithmic question in this area is deciding whether a given permutation of length n contains a given pattern of length k.  ...  Our algorithms can also count, within the same running time, the number of occurrences of a pattern.  ...  Acknowledgements An earlier version of the paper contained a mistake in the analysis of the algorithm for Theorem 2. We thank Günter Rote for pointing out the error.  ... 
doi:10.1007/s00453-021-00812-z fatcat:owcrk6hapbcvjp3nv5ydv7jsrm
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