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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
An asymptotic theory for CauchyEuler differential equations with applications to the analysis of algorithms
, 2002
"... CauchyEuler differential equations surfaced naturally in a number of sorting and searching problems, notably in quicksort and binary search trees and their variations. Asymptotics of coefficients of functions satisfying such equations has been studied for several special cases in the literature. We ..."
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Cited by 23 (10 self)
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CauchyEuler differential equations surfaced naturally in a number of sorting and searching problems, notably in quicksort and binary search trees and their variations. Asymptotics of coefficients of functions satisfying such equations has been studied for several special cases in the literature. We study in this paper the most general framework for CauchyEuler equations and propose an asymptotic theory that covers almost all applications where CauchyEuler equations appear. Our approach is very general and requires almost no background on differential equations. Indeed the whole theory can be stated in terms of recurrences instead of functions. Old and new applications of the theory are given. New phase changes of limit laws of new variations of quicksort are systematically derived. We apply our theory to about a dozen of diverse examples in quicksort, binary search trees, urn models, increasing trees, etc.
A Note on Synthesis and Classification of Sorting Algorithms
 Acta Informatica
, 1989
"... this paper, and the referees for their very helpful comments and constructive suggestions which greatly improved an earlier version of this paper. References ..."
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Cited by 7 (4 self)
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this paper, and the referees for their very helpful comments and constructive suggestions which greatly improved an earlier version of this paper. References
Topdown Synthesis of Sorting Algorithms
, 1992
"... Traditionally sorting algorithms are classified according to their main operational characteristic, rather than their underlying logic. More recent work in program synthesis has exposed the logic of and hence the logical relationships between some sorting algorithms. Following the program synthesis ..."
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Cited by 5 (2 self)
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Traditionally sorting algorithms are classified according to their main operational characteristic, rather than their underlying logic. More recent work in program synthesis has exposed the logic of and hence the logical relationships between some sorting algorithms. Following the program synthesis approach, and by using a logic programming system for deriving recursive logic procedures from their specifications, we have synthesised a large family of sorting algorithms in a strictly topdown manner. Such an approach not only produces algorithms which are guaranteed to be partially correct, it also provides a family tree showing clearly the relationships between its members. This paper contains c.4500 words, 15 pages, and 1 diagram. 1 Introduction Traditionally, algorithms are "discovered" first, and then proved correct. Sorting algorithms are no exception. More recently, work in program synthesis has been applied to the derivation of algorithms from their specifications. The main adva...
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.
KSort: A New Sorting Algorithm that Beats Heap Sort for n ��70 Lakhs!
"... Abstract Sundararajan and Chakraborty [10] introduced a new version of Quick sort removing the interchanges. Khreisat [6] found this algorithm to be competing well with some other versions of Quick sort. However, it uses an auxiliary array thereby increasing the space complexity. Here, we provide a ..."
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Abstract Sundararajan and Chakraborty [10] introduced a new version of Quick sort removing the interchanges. Khreisat [6] found this algorithm to be competing well with some other versions of Quick sort. However, it uses an auxiliary array thereby increasing the space complexity. Here, we provide a second version of our new sort where we have removed the auxiliary array. This second improved version of the algorithm, which we call Ksort, is found to sort elements faster than Heap sort for an appreciably large array size (n � � 70,00,000) for uniform U[0, 1] inputs. Index Terms Internal sorting, uniform distribution, average time complexity, statistical analysis, statistical bound. I.