A survey of adaptive sorting algorithms
ACM Computing Surveys (CSUR)
Trans-dichotomous algorithms for minimum spanning trees and shortest paths
Journal of Computer and System Sciences - Special issue: 31st IEEE conference on foundations of computer science, Oct. 22–24, 1990
The art of computer programming, volume 3: (2nd ed.) sorting and searching
The art of computer programming, volume 3: (2nd ed.) sorting and searching
Implicit Data Structures for the Dictionary Problem
Journal of the ACM (JACM)
Best sorting algorithm for nearly sorted lists
Communications of the ACM
Optimal Algorithms for List Indexing and Subset Rank
WADS '89 Proceedings of the Workshop on Algorithms and Data Structures
Succinct Dynamic Data Structures
WADS '01 Proceedings of the 7th International Workshop on Algorithms and Data Structures
Two Simplified Algorithms for Maintaining Order in a List
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Implicit data structures (Preliminary Draft)
STOC '79 Proceedings of the eleventh annual ACM symposium on Theory of computing
Fun-sort--or the chaos of unordered binary search
Discrete Applied Mathematics - Fun with algorithms 2 (FUN 2001)
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This paper investigates how to improve the worst case runtime of Insertion Sort while keeping it in-place, incremental and adaptive. To sort an array of n elements with w bits for each element, classic Insertion Sort runs in O(n2) operations with wn bits space. Gapped Insertion Sort has a runtime of O(n lg n) with a high probability of only using (1 + ε)wn bits space. This paper shows that Rotated Insertion Sort guarantees O(√n lg n) operations per insertion and has a worst case sorting time of O(n1.5 lg n) operations by using optimal O(w) auxiliary bits. By using extra Θ(√n lg n) bits and recursively applying the same structure l times, it can be done with O(2l n1+1/l) operations. Apart from the space usage and time guarantees, it also has the advantage of efficiently retrieving the i-th element in constant time. This paper presents Rotated Library Sort that combines the advantages of the above two improved approaches.