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A linear time algorithm for consecutive permutation pattern matching

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*. ...

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

2015
*
arXiv
*
pre-print

We give

arXiv:1511.01770v1
fatcat:5vsxmo5vszd4nd3lz2mb4k4vie
*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*. ...##
###
Testing for the consecutive ones property, interval graphs, and graph planarity using PQ-tree algorithms

1976
*
Journal of computer and system sciences (Print)
*

The

doi:10.1016/s0022-0000(76)80045-1
fatcat:rvplpslsifa7hcvvc572m4ldy4
*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. ...##
###
The computational landscape of permutation patterns
[article]

2014
*
arXiv
*
pre-print

In this paper we draw

arXiv:1301.0340v2
fatcat:of4huwt4dna2vd2gusyvpxpm5e
*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 ...##
###
A Note on Scoring Clones Given a Probe Ordering

1995
*
Journal of Computational Biology
*

The

doi:10.1089/cmb.1995.2.33
pmid:7497118
fatcat:t2epcnnsonbf7pj4e4mzm7eagy
*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*. ...##
###
Permutation Pattern matching in (213, 231)-avoiding permutations

2017
*
Discrete Mathematics & Theoretical Computer Science
*

We give

doi:10.46298/dmtcs.1329
fatcat:wo7fipgr4zazbpxebdpinysk3a
*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*. ...##
###
Pattern Matching for Separable Permutations
[chapter]

2016
*
Lecture Notes in Computer Science
*

This improves upon the existing O(n 8 )

doi:10.1007/978-3-319-46049-9_25
fatcat:73qkwvhanjgobegpfqmxvfk3f4
*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] ). ...##
###
Single and Multiple Consecutive Permutation Motif Search
[chapter]

2013
*
Lecture Notes in Computer Science
*

We then extend the problem to search

doi:10.1007/978-3-642-45030-3_7
fatcat:ih43vxy6ifdg7mu7jejz37odeu
*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. ...##
###
Faster Exponential Algorithm for Permutation Pattern Matching
[article]

2021
*
arXiv
*
pre-print

The

arXiv:2108.11475v1
fatcat:qwmzto4s2vddxlfleq2ehfffr4
*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. ...##
###
Sub-quadratic time and linear space data structures for permutation matching in binary strings

2012
*
Journal of Discrete Algorithms
*

Given

doi:10.1016/j.jda.2011.08.003
fatcat:aiy4c2t27zginovpxeccctlyra
*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] . ...##
###
Counting preimages of TCP reordering patterns

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. ...

##
###
PQR sort: using PQR trees for binary matrix reorganization

2014
*
Journal of the Brazilian Computer Society
*

Results: We found that PQR sort is an interesting method

doi:10.1186/1678-4804-20-3
fatcat:qo4o23tpw5eihi6kabiv33s5cm
*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*. ...##
###
Minimising the number of gap-zeros in binary matrices

2013
*
European Journal of Operational Research
*

We study

doi:10.1016/j.ejor.2013.01.028
fatcat:e73sregpsnd43gtwwvp3ttci4a
*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. ...##
###
Finding and counting permutations via CSPs
[article]

2019
*
arXiv
*
pre-print

Perhaps the most natural

arXiv:1908.04673v1
fatcat:uzraxyou3jdybawbiojy3l2gk4
*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. ...##
###
Finding and Counting Permutations via CSPs

2021
*
Algorithmica
*

Perhaps the most natural

doi:10.1007/s00453-021-00812-z
fatcat:owcrk6hapbcvjp3nv5ydv7jsrm
*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. ...
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