An implicit data structure supporting insertion, deletion, and search in O(log:OS2:OEn) time
Journal of Computer and System Sciences
No. 318 on SWAT 88: 1st Scandinavian workshop on algorithm theory
Journal of the ACM (JACM)
Randomized algorithms
Exploiting few inversions when sorting: sequential and parallel algorithms
Theoretical Computer Science
Analysis of Hoare's FIND algorithm with median-of-three partition
Random Structures & Algorithms - Special issue: average-case analysis of algorithms
In-place sorting with fewer moves
Information Processing Letters
An efficient dynamic selection method
Communications of the ACM
Expected time bounds for selection
Communications of the ACM
Communications of the ACM
Asymptotically efficient in-place merging
Theoretical Computer Science
Nordic Journal of Computing
Linear-time In-place Selection in Less than 3n Comparisons
ISAAC '95 Proceedings of the 6th International Symposium on Algorithms and Computation
Journal of Computer and System Sciences
Journal of Computer and System Sciences
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A variant of the classical selection problem, called the positioning problem, is considered. In this problem we are given a sequence A[1:n] of size n, an integer k, 1 驴 k 驴 n, and an ordering function ???, and the task is to rearrange the elements of the sequence such that A[k]??? A[j] is false for all j, 1 驴 j 驴 k, and A[l]??? A[k] is false for all l, k l 驴 n. We present a Las-Vegas algorithm which carries out this rearrangement efficiently using only a constant amount of additional space even if the input contains equal elements and if only pairwise element comparisons are permitted. To be more precise, the algorithm solves the positioning problem in-place in linear time using at most n + k + o(n) element comparisons, k + o(n) element exchanges, and the probability for succeeding within stated time bounds is at least 1 - e-n驴(1).