A survey of adaptive sorting algorithms

Estivill‐Castro, Vladimir; Wood, Derick

doi:10.1145/146370.146381

Cited by 161 publications

(99 citation statements)

References 30 publications

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“…This completes the construction of the point set P, and we consider the planar convex hull problem when the input array is P. Let Q be the output array. Then we can see that P [1], P [2] and P [3] are the points on the boundary of the convex hull, and k = inv(≤ P , ≤ Q ). Furthermore, from Q we can extract the sorted sequence in the increasing order as the x-coordinates of Q [4..n+3].…”

Section: Theorem 3 Any Algorithm To Solve the Planar Convex Hull Promentioning

confidence: 99%

“…Mehlhorn [1] introduced the term "adaptive sorting algorithms" for those with such a property. A formal framework for the worst-case analysis of adaptive sorting algorithms was introduced by Mannila [2], and the framework is well surveyed by Estivill-Castro and Wood [3]. An adaptive sorting algorithm has several characteristics.…”

Section: Introductionmentioning

confidence: 99%

“…Several "presortedness" measures have been proposed [3]. In this work, we use the oldest and the most frequently used measure: the number of inversions.…”

Section: Introductionmentioning

confidence: 99%

“…We recommend the readers to consult a survey by Estivill-Castro and Wood [3]. Adaptive sorting algorithms are also discussed in terms of integer sorting [7] and I/O-efficiency (both cache-aware and cacheoblivious) [8].…”

Section: Introductionmentioning

confidence: 99%

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Adaptive Algorithms for Planar Convex Hull Problems

Ahn

Okamoto

2011

IEICE Trans. Inf. & Syst.

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SUMMARYWe study problems in computational geometry from the viewpoint of adaptive algorithms. Adaptive algorithms have been extensively studied for the sorting problem, and in this paper we generalize the framework to geometric problems. To this end, we think of geometric problems as permutation (or rearrangement) problems of arrays, and define the "presortedness" as a distance from the input array to the desired output array. We call an algorithm adaptive if it runs faster when a given input array is closer to the desired output, and furthermore it does not make use of any information of the presortedness. As a case study, we look into the planar convex hull problem for which we discover two natural formulations as permutation problems. An interesting phenomenon that we prove is that for one formulation the problem can be solved adaptively, but for the other formulation no adaptive algorithm can be better than an optimal outputsensitive algorithm for the planar convex hull problem. To further pursue the possibility of adaptive computational geometry, we also consider constructing a kd-tree. key words: adaptive algorithms, convex hulls, computational geometry

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Section: Theorem 3 Any Algorithm To Solve the Planar Convex Hull Promentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…Several "presortedness" measures have been proposed [3]. In this work, we use the oldest and the most frequently used measure: the number of inversions.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Adaptive Algorithms for Planar Convex Hull Problems

Ahn

Okamoto

2011

IEICE Trans. Inf. & Syst.

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“…We will also need a standard measure of disorder in almost-sorted sequences [4]. This measure has the name shuffled up-sequences (SUS).…”

Section: Identifying Almost Sorted Permutations From Tcp Buffer Dynammentioning

confidence: 99%

Identifying Almost Sorted Permutations from TCP Buffer Dynamics

Istrate¹

2015

SACS

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Associate to each sequence A of integers (intending to model packet IDs in a TCP/IP stream) a sequence of positive integers of the same length M(A). The i'th entry of M(A) is the size (at time i) of the smallest buffer needed to hold out-of-order packets, where space is accounted for unreceived packets as well. Call two sequences A, B equivalent (writtenFor a sequence of integers A define SUS(A) to be the shuffled-upsequences reordering measure defined as the smallest possible number of classes in a partition of the original sequence into increasing subsequences. We prove the following result: any two permutations A, B of the same length with SUS(A), SUS(B) ≤ 3 such that A ≡ F B B are identical. The result is no longer valid if we replace the upper bound 3 by 4.We also consider a similar problem for permutations with repeats. In this case the uniqueness of the preimage is no longer true, but we obtain a characterization of all the preimages of a given sequence, which in particular allows us to count them in polynomial time.The results were motivated by explaining the behavior and engineering Restored, a receiver-oriented model of traffic we introduced and experimentally validated in earlier work.

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A Nonoblivious Bus Access Scheme Yields an Optimal Partial Sorting Algorithm

Fujita

Yamashita

1996

Journal of Parallel and Distributed Computing

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A survey of adaptive sorting algorithms

Cited by 161 publications

References 30 publications

Adaptive Algorithms for Planar Convex Hull Problems

Adaptive Algorithms for Planar Convex Hull Problems

Identifying Almost Sorted Permutations from TCP Buffer Dynamics

A Nonoblivious Bus Access Scheme Yields an Optimal Partial Sorting Algorithm

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