An efficient dynamic selection method
Communications of the ACM
Expected time bounds for selection
Communications of the ACM
A sorting problem and its complexity
Communications of the ACM
Communications of the ACM
Finding the median requires 2n comparisons
STOC '85 Proceedings of the seventeenth annual ACM symposium on Theory of computing
Optimal sample cost residues for differential database batch query problems
Journal of the ACM (JACM)
Deterministic sorting and randomized median finding on the BSP model
Proceedings of the eighth annual ACM symposium on Parallel algorithms and architectures
Architecture independent parallel selection with applications to parallel priority queues
Theoretical Computer Science
Randomized selection in n + C + o(n) comparisons
Information Processing Letters
| Hi-index | 0.01 |
We consider problems such as selecting the k-th smallest of n numbers in as few comparisons as possible on average. n + k - 0(1) comparisons are proved to be necessary for this particular problem when k ≤ n/2. This shows a technique of Floyd and Rivest is essentially optimal. 7n/4 &equil; o(n) comparisons, on average, are shown to be necessary and sufficient to find the maximum and median of a set. An upper bound of 9n/4 + o(n) and a lower bound of 2n − o(n) are shown for the max-min-median problem.