Finding the median requires 2n comparisons
STOC '85 Proceedings of the seventeenth annual ACM symposium on Theory of computing
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
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Minimizing randomness in minimum spanning tree, parallel connectivity, and set maxima algorithms
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
A Randomized In-Place Algorithm for Positioning the kth Element in a Multiset
SWAT '02 Proceedings of the 8th Scandinavian Workshop on Algorithm Theory
An Efficient Algorithm for the Approximate Median Selection Problem
CIAC '00 Proceedings of the 4th Italian Conference on Algorithms and Complexity
On Floyd and Rivest's SELECT algorithm
Theoretical Computer Science
Randomized minimum spanning tree algorithms using exponentially fewer random bits
ACM Transactions on Algorithms (TALG)
Comparison-based time-space lower bounds for selection
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Comparison-based time-space lower bounds for selection
ACM Transactions on Algorithms (TALG)
Adaptive sampling strategies for quickselects
ACM Transactions on Algorithms (TALG)
Towards optimal multiple selection
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
| Hi-index | 0.01 |
It is shown that n + k - O(1) comparisons are necessary, on average, to find the kth smallest of n numbers (k ⪇ n/2). This lower bound matches the behavior of the technique of Floyd and Rivest to within a lower-order term. 7n/4 ± 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.