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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
Inorder Traversal of a Binary Heap and its Inversion in Optimal Time and Space
 Mathematics of Program Construction, volume 669 of Lecture Notes in Computer Science
, 1992
"... In this paper we derive a lineartime, constantspace algorithm to construct a binary heap whose inorder traversal equals a given sequence. We do so in two steps. First, we invert a program that computes the inorder traversal of a binary heap, using the proof rules for program inversion by W. Chen a ..."
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Cited by 5 (0 self)
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In this paper we derive a lineartime, constantspace algorithm to construct a binary heap whose inorder traversal equals a given sequence. We do so in two steps. First, we invert a program that computes the inorder traversal of a binary heap, using the proof rules for program inversion by W. Chen and J.T. Udding. This results in a lineartime solution in terms of binary trees. Subsequently, we datarefine this program to a constantspace solution in terms of linked structures. 1
Quadratic Integer Programming with Application in the Chaotic Mappings of Complete Multipartite Graphs
"... Let a be a permutation of the vertex set V (G) of a connected graph G. Define the total relative displacement of a in G by where dG (x;y) is the length of the shortest path between x and y in G. Let p (G) be the maximum value of d a (G) among all permutations of V (G). The permutation which ..."
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Cited by 2 (0 self)
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Let a be a permutation of the vertex set V (G) of a connected graph G. Define the total relative displacement of a in G by where dG (x;y) is the length of the shortest path between x and y in G. Let p (G) be the maximum value of d a (G) among all permutations of V (G). The permutation which realizes (G) is called a chaotic mapping of G. In this paper, we study the chaotic mappings of complete multipartite graphs. The problem will be reduced to a quadratic integer programming problem. We characterize its optimal solution and present an algorithm running logn) time where n is the total number of vertices in a complete multipartite graph.
The Expected Variation of Random Bounded Integer Sequences of Finite Length 1
"... From the enumerative generating function of an abstract adjacency statistic, we deduce the mean and variance of the variation on random permutations, rearrangements, compositions, and bounded integer sequences of finite length. Key words sequence variation, sequence oscillation, adjacency 1 ..."
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Cited by 1 (1 self)
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From the enumerative generating function of an abstract adjacency statistic, we deduce the mean and variance of the variation on random permutations, rearrangements, compositions, and bounded integer sequences of finite length. Key words sequence variation, sequence oscillation, adjacency 1