Permutations Sorted by a Finite and an Infinite Stack in Series

Elder, Murray; Goh, Yoong Kuan

doi:10.1007/978-3-319-77313-1_17

Cited by 5 publications

(4 citation statements)

References 14 publications

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“…We make the following observations. First, our present result is in contrast to the usual (nondeterministic) stacks-in-series model where in many cases no finite pattern-avoidance characterisation is possible due to the existence of infinite antichains [3,9]. Second, the operation of a pop stack is related to classical sorting: "bubble-sort" is exactly sorting by arbitrarily many passes through a pop stack of depth 2.…”

Section: Introductionmentioning

confidence: 72%

$k$-pop stack sortable permutations and $2$-avoidance

Elder¹,

Goh²

2019

Preprint

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We consider permutations sortable by k passes through a deterministic pop stack. We show that for any k ∈ N the set is characterised by finitely many patterns, answering a question of Claesson and Guðmundsson.Our characterisation demands a more precise definition than in previous literature of what it means for a permutation to avoid a set of barred and unbarred patterns. We propose a new notion called 2-avoidance.

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Section: Introductionmentioning

confidence: 72%

$k$-pop stack sortable permutations and $2$-avoidance

Elder¹,

Goh²

2019

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…We make the following observations. First, our present result is in contrast to the usual (nondeterministic) stacks-in-series model where in many cases no finite pattern-avoidance characterisation is possible due to the existence of infinite antichains [4,10]. Second, the operation of a pop stack is related to classical sorting: "bubble-sort" is exactly sorting by arbitrarily many passes through a pop stack of depth 2.…”

Section: Introductionmentioning

confidence: 74%

$k$-Pop Stack Sortable Permutations and $2$-Avoidance

Elder

Goh

2021

Electron. J. Combin.

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We consider permutations sortable by $k$ passes through a deterministic pop stack. We show that for any $k\in\mathbb{N}$ the set is characterised by finitely many patterns, answering a question of Claesson and Guðmundsson. Moreover, these sets of patterns are algorithmically constructible. Our characterisation demands a more precise definition than in previous literature of what it means for a permutation to avoid a set of barred and unbarred patterns. We propose a new notion called $2$-avoidance.

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“…Conversely, the approximate positions of ordered data can be provided when using the values as inputs. Elder and Goh (2018) studied permutation sorting by finite and infinite stacks. Although all possible permutations cannot be sorted, the exact order and values can be obtained.…”

Section: Introductionmentioning

confidence: 99%

Peer Review #1 of "Correct and stable sorting for overflow streaming data with a limited storage size and a uniprocessor (v0.2)"

2021

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Tremendous quantities of numeric data have been generated as streams in various cyber ecosystems. Sorting is one of the most fundamental operations to gain knowledge from data. However, due to size restrictions of data storage which includes storage inside and outside CPU with respect to the massive streaming data sources, data can obviously overflow the storage. Consequently, all classic sorting algorithms of the past are incapable of obtaining a correct sorted sequence because data to be sorted can not be totally stored in the data storage. This paper proposes a new sorting algorithm called streaming data sort for streaming data on a uniprocessor constrained by a limited storage size and the correctness of the sorted order. Data continuously flow into the storage as consecutive chunks with chunk sizes less than the storage size. A theoretical analysis of the space bound and the time complexity is provided. The sorting time complexity is O ( n ) " role="presentation" style="position: relative;"> O ( n ) O ( n ) O(n) , where n " role="presentation" style="position: relative;"> n n n is the number of incoming data. The space complexity is O ( M ) " role="presentation" style="position: relative;"> O ( M ) O ( M ) O(M) , where M " role="presentation" style="position: relative;"> M M M is the storage size. The experimental results show that streaming data sort can handle a million permuted data by using a storage whose size is set as low as 35% of the data size. This proposedconcept can be practically applied to various applications in different fields where the data always overflowthe working storage and sorting process is needed.

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Permutations Sorted by a Finite and an Infinite Stack in Series

Cited by 5 publications

References 14 publications

$k$-pop stack sortable permutations and $2$-avoidance

$k$-pop stack sortable permutations and $2$-avoidance

$k$-Pop Stack Sortable Permutations and $2$-Avoidance

Peer Review #1 of "Correct and stable sorting for overflow streaming data with a limited storage size and a uniprocessor (v0.2)"

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