Finding the ith largest of n for small i,n
ACM SIGACT News
The art of computer programming, volume 3: (2nd ed.) sorting and searching
The art of computer programming, volume 3: (2nd ed.) sorting and searching
Sorting 13 Elements Requires 34 Comparisons
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
An Efficient Algorithm for the Approximate Median Selection Problem
CIAC '00 Proceedings of the 4th Italian Conference on Algorithms and Complexity
Dynamic Programming
Further analysis of the remedian algorithm
Theoretical Computer Science
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We show how to find optimal algorithms for the selection of one or more order statistics over a small set of numbers, and as an extreme case, complete sorting. The criterion is using the smallest number of comparisons; separate derivations are performed for minimization on the average (over all permutations) or in the worst case. When the computational process establishes the optimal values, it also generates C-language functions that implement policies which achieve those optimal values. The search for the algorithms is driven by a Markov decision process, and the program provides the optimality proof as well.