Insertion Sort is O(n log n)

Bender, Michael A.; Farach-Colton, Martı́n; Mosteiro, Miguel A.

doi:10.1007/s00224-005-1237-z

Cited by 47 publications

(16 citation statements)

References 10 publications

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“…We also re-implemented the rebalancing algorithm of [10], marked in the graph as APMA 7 . In Figure 11a, there are only marginal differences w.r.t.…”

Section: Discussionmentioning

confidence: 99%

“…The memory footprint of the RMA, with the ST, is about 1.4x bigger than static dense arrays. With the UT, the difference varies, up to 2x the optimal space of dense 7 The original source code of APMA was never openly released by [10].…”

Section: Discussionmentioning

confidence: 99%

“…The tightest bounds for the data structure are based on amortised analysis. In the RAM model, given C the capacity of the underlying array, updates feature O(log 2 2 C) in worst case amortised analysis per update operation [4], [18], and, if the keys follow a uniform distribution, O(log 2 C) in average amortised analysis [7], [18]. In fact, because the number of elements N stored at any time is proportional to the capacity C of the array, i.e.…”

Section: Preliminariesmentioning

confidence: 99%

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Packed Memory Arrays - Rewired

Leo

Boncz

2019

2019 IEEE 35th International Conference on Data Engineering (ICDE)

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The physical memory layout of a tree-based index structure deteriorates over time as it sustains more updates; such that sequential scans on the physical level become nonsequential, and therefore slower. Packed Memory Arrays (PMAs) prevent this by managing all data in a sequential sparse array. PMAs have been studied mostly theoretically but suffer from practical problems, as we show in this paper. We study and fix these problems, resulting in an improved data structure: the Rewired Memory Array (RMA). We compare RMA with the main previous PMA implementations as well as state-of-the-art tree index structures and show on a wide variety of data and query distributions that RMA can reach competitive update and point lookup performance, while always providing superior scan performance -close to dense column scans.

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“…We also re-implemented the rebalancing algorithm of [10], marked in the graph as APMA 7 . In Figure 11a, there are only marginal differences w.r.t.…”

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Preliminariesmentioning

confidence: 99%

See 1 more Smart Citation

Packed Memory Arrays - Rewired

Leo

Boncz

2019

2019 IEEE 35th International Conference on Data Engineering (ICDE)

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“…Improvements to algorithms taught at the undergraduate level are still being published. For example, a new sorting algorithm, the Library Sort [2], was published in 2006. Students will continue to uncover new strategies to solve classic problems, and the challenge to teachers and supporting software is responding appropriately to unique solution strategies that may originate with students.…”

Section: Discussionmentioning

confidence: 99%

Toward facilitating assistance to students attempting engineering design problems

Glassman

Gulley

Miller

2013

Proceedings of the Ninth Annual International ACM Conference on International Computing Education Research

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In engineering design courses, many problems have a specification that the student's implementation must meet, but give the student a large range of freedom for the internal design of that implementation. There may be several distinct, correct strategies for solving them, some of which may be unknown to the teaching staff or intelligent tutor designer. When a student is pursuing an unrecognized strategy and begins to struggle, staff may redirect them, costing unnecessary work, and automated hint generators may offer unhelpful feedback. We have taken a first step toward discovering these alternate correct strategies by visualizing many student solutions together, using dynamic and static features of these solutions, so that the teaching staff can understand the space of correct strategies. This approach has been applied to two domains: an online Matlab programming challenge and an undergraduate computer architecture course. We discuss these initial investigations and pose discussion questions to the community about potential enhancement and application of this analysis.

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“…Even simpler rebalance schemes perform well under random inserts, as shown in [7,14]. These papers show that there are O(log N) moves with high probability for random inserts, even with the most basic of rebalances: When we insert an element y after an element x, we simply push the elements to the right or left to make room for y.…”

Section: Theorem 5 ( [7 14]) For Random Inserts With High Probabilmentioning

confidence: 95%

An adaptive packed-memory array

Bender

2006

Proceedings of the Twenty-Fifth ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems

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The packed-memory array (PMA) is a data structure that maintains a dynamic set of N elements in sorted order in a Θ(N)-sized array. The idea is to intersperse Θ(N) empty spaces or gaps among the elements so that only a small number of elements need to be shifted around on an insert or delete. Because the elements are stored physically in sorted order in memory or on disk, the PMA can be used to support extremely efficient range queries. Specifically, the cost to scan L consecutive elements is O(1 + L/B) memory transfers.This paper gives the first adaptive packed-memory array (APMA), which automatically adjusts to the input pattern. Like the original PMA, any pattern of updates costs only O(log 2 N) amortized element moves and O(1 + (log 2 N)/B) amortized memory transfers per update. However, the APMA performs even better on many common input distributions achieving only O(log N) amortized element moves and O(1 + (log N)/B) amortized memory transfers. The paper analyzes sequential inserts, where the insertions are to the front of the APMA, hammer inserts, where the insertions "hammer" on one part of the APMA, random inserts, where the insertions are after random elements in the APMA, and bulk inserts, where for constant α ∈ [0, 1], N α elements are inserted after random elements in the APMA. The paper then gives simulation results that are consistent with the asymptotic bounds. For sequential insertions of roughly 1.4 million elements, the APMA has four times fewer element moves per insertion than the traditional PMA and running times that are more than seven times faster.

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Insertion Sort is O(n log n)

Cited by 47 publications

References 10 publications

Packed Memory Arrays - Rewired

Packed Memory Arrays - Rewired

Toward facilitating assistance to students attempting engineering design problems

An adaptive packed-memory array

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