A linear time algorithm for consecutive permutation pattern matching

Kubica, Marcin; Kulczyński, Tomasz; Radoszewski, Jakub; Rytter, Wojciech; Waleń, Tomasz

doi:10.1016/j.ipl.2013.03.015

Cited by 69 publications

(106 citation statements)

References 7 publications

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“…An O(k 2 n 6 )-time algorithm is presented in [21] for the case that both the text and the pattern that do not contain 321. If the pattern is required to be matched to consecutive elements in the text, a O(n + k) algorithm has been found [28]. A similar result has been found independently in [24].…”

Section: Questionsupporting

confidence: 56%

A Fast Algorithm for Permutation Pattern Matching Based on Alternating Runs

Bruner

Lackner

2015

Algorithmica

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The NP-complete Permutation Pattern Matching problem asks whether a k-permutation P is contained in a n-permutation T as a pattern. This is the case if there exists an order-preserving embedding of P into T . In this paper, we present a fixed-parameter algorithm solving this problem with a worst-case runtime of O(1.79 run(T ) · n · k), where run(T ) denotes the number of alternating runs of T . This algorithm is particularly well-suited for instances where T has few runs, i.e., few ups and downs. Moreover, since run(T ) < n, this can be seen as a O(1.79 n · n · k) algorithm which is the first to beat the exponential 2 n runtime of brute-force search. Furthermore, we prove that under standard complexity theoretic assumptions such a fixedparameter tractability result is not possible for run(P ).

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Section: Questionsupporting

confidence: 56%

A Fast Algorithm for Permutation Pattern Matching Based on Alternating Runs

Bruner

Lackner

2015

Algorithmica

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“…For a string x 2 ⌃ ⇤ , let |x| denote the length of x. A string x is described by a sequence of characters ( Order Isomorphism [7] For two strings x and y of length n, x and y are order-…”

Section: Problem Formulationmentioning

confidence: 99%

“…The order relation between two characters is a ternary relation (>, <, =) rather than a binary relation (>, <), but it was not su ciently studied in previous works [5,7,1]. In this paper, we extend the representations of order relations by Kim et al…”

Section: Introductionmentioning

confidence: 96%

“…It has many practical applications such as stock price analysis and musical melody matching. The study on this field was introduced by Kubica et al [7] and Kim et al [5] where Kubica et al [7] defined order relations by order isomorphism of two strings, while Kim et al [5] defined them explicitly by the sequence Copyright c by the paper's authors. Copying permitted only for private and academic purposes.…”

Section: Introductionmentioning

confidence: 99%

“…Kim et al [5] considered only binary order relations by assuming that all the characters in a string are distinct, while Kubica et al [7] considered ternary order relations but their match condition on equal characters was faulty and it was fixed later by Cho et al [1]. As there was no integrated study on the relationship between the representations of order relations, previous works [1,2,3] individually handled the cumbersome details of ternary order relations on their own works.…”

Section: Introductionmentioning

confidence: 99%

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On Representations of Ternary Order Relations in Numeric Strings

Kim

Amir

et al. 2017

Math.Comput.Sci.

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Order-preserving matching is a string matching problem of two numeric strings where the relative orders of consecutive substrings are matched instead of the characters themselves. The order relation between two characters is a ternary relation (>, <, =) rather than a binary relation (>, <), but it was not su ciently studied in previous works [5,7,1]. In this paper, we extend the representations of order relations by Kim et al.[5] to ternary order relations, and prove the equivalence of those representations. The extended prefix representation takes log m + 1 bits per character, while the nearest neighbor representation takes 2 log m bits per character. With our extensions, the time complexities of order-preserving matching in binary order relations can be achieved in ternary order relations as well.

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Engineering order‐preserving pattern matching with SIMD parallelism

et al. 2016

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SUMMARYThe order-preserving pattern matching problem has gained attention in recent years. It consists in finding all substrings in the text, which have the same length and relative order as the input pattern. Typically, the text and the pattern consist of numbers. Since recent times, there has been a tendency to utilize the ability of the word RAM model to increase the efficiency of string matching algorithms. This model works on computer words, reading and processing blocks of characters at once, so that usual arithmetic and logic operations on words can be performed in one unit of time. In this paper, we present a fast order-preserving pattern matching algorithm, which uses specialized word-size packed string matching instructions, grounded on the single instruction multiple data instruction set architecture. We show with experimental results that the new proposed algorithm is more efficient than the previous solutions.

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A linear time algorithm for consecutive permutation pattern matching

Cited by 69 publications

References 7 publications

A Fast Algorithm for Permutation Pattern Matching Based on Alternating Runs

A Fast Algorithm for Permutation Pattern Matching Based on Alternating Runs

On Representations of Ternary Order Relations in Numeric Strings

Engineering order‐preserving pattern matching with SIMD parallelism

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