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A Survey of Adaptive Sorting Algorithms
, 1992
"... Introduction and Survey; F.2.2 [Analysis of Algorithms and Problem Complexity]: Nonnumerical Algorithms and Problems  Sorting and Searching; E.5 [Data]: Files  Sorting/searching; G.3 [Mathematics of Computing]: Probability and Statistics  Probabilistic algorithms; E.2 [Data Storage Represe ..."
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Cited by 65 (3 self)
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Introduction and Survey; F.2.2 [Analysis of Algorithms and Problem Complexity]: Nonnumerical Algorithms and Problems  Sorting and Searching; E.5 [Data]: Files  Sorting/searching; G.3 [Mathematics of Computing]: Probability and Statistics  Probabilistic algorithms; E.2 [Data Storage Representation]: Composite structures, linked representations. General Terms: Algorithms, Theory. Additional Key Words and Phrases: Adaptive sorting algorithms, Comparison trees, Measures of disorder, Nearly sorted sequences, Randomized algorithms. A Survey of Adaptive Sorting Algorithms 2 CONTENTS INTRODUCTION I.1 Optimal adaptivity I.2 Measures of disorder I.3 Organization of the paper 1.WORSTCASE ADAPTIVE (INTERNAL) SORTING ALGORITHMS 1.1 Generic Sort 1.2 CookKim division 1.3 Partition Sort 1.4 Exponential Search 1.5 Adaptive Merging 2.EXPECTEDCASE ADAPTIV
Cacheaware and cacheoblivious adaptive sorting
 In Proc. 32nd International Colloquium on Automata, Languages, and Programming, Lecture Notes in Computer Science
, 2005
"... Abstract. Two new adaptive sorting algorithms are introduced which perform an optimal number of comparisons with respect to the number of inversions in the input. The first algorithm is based on a new linear time reduction to (nonadaptive) sorting. The second algorithm is based on a new division pr ..."
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Cited by 11 (4 self)
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Abstract. Two new adaptive sorting algorithms are introduced which perform an optimal number of comparisons with respect to the number of inversions in the input. The first algorithm is based on a new linear time reduction to (nonadaptive) sorting. The second algorithm is based on a new division protocol for the GenericSort algorithm by EstivillCastro and Wood. From both algorithms we derive I/Ooptimal cacheaware and cacheoblivious adaptive sorting algorithms. These are the first I/Ooptimal adaptive sorting algorithms. 1
A HeapBased Optimal InversionsSensitive Sorting Algorithm
, 2003
"... this paper, we describe a new timeoptimal algorithm that makes n lg(I=n) + O(n lg lg(I=n) + n) comparisons. This is an optimal algorithm for inversionssensitive sorting in the sense that it is timeoptimal and the number of comparisons it performs matches the informationtheoretic lower bound up t ..."
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this paper, we describe a new timeoptimal algorithm that makes n lg(I=n) + O(n lg lg(I=n) + n) comparisons. This is an optimal algorithm for inversionssensitive sorting in the sense that it is timeoptimal and the number of comparisons it performs matches the informationtheoretic lower bound up to lower order terms. (To be precise, the number of comparisons performed by our algorithm is optimal with respect to its leading term and near optimal with respect to the second term. This is explained in the following section.) 2 Earlier Results Adaptive sorting using the nger trees data structure introduced in [GMPR77], was the rst inversionssensitive timeoptimal sorting algorithm. Mehlhorn [Me79] introduced an algorithm with the same time bounds as nger trees. Both of these algorithms are considered impractical. As summarized by Elmasry [El02], other algorithms that are timeoptimal and inversionssensitive are Blocksort [LP96] which runs in place and treebased Mergesort [MEP96] which is timeoptimal with respect to several other measures of presortedness
and
"... We study the performance of the most practical inversionsensitive internal sorting algorithms. Experimental results illustrate that adaptive AVL sort consumes the fewest number of comparisons unless the number of inversions is less than 1%; in such case Splaysort consumes the fewest number of compa ..."
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We study the performance of the most practical inversionsensitive internal sorting algorithms. Experimental results illustrate that adaptive AVL sort consumes the fewest number of comparisons unless the number of inversions is less than 1%; in such case Splaysort consumes the fewest number of comparisons. On the other hand, the running time of Quicksort is superior unless the number of inversions is less than 1.5%; in such case Splaysort has the shortest running time. Another interesting result is that although the number of cache misses for the cacheoptimal Greedysort algorithm was the least, compared to other adaptive sorting algorithms under investigation, it was outperformed by Quicksort.