Journal ArticleDOI
Average case selection
Walter Cunto,J. Ian Munro +1 more
TLDR
It is shown that n + k - O comparisons are necessary, on average, to find the smallest of n numbers and this lower bound matches the behavior of the technique of Floyd and Rivest to within a lower-order term.Abstract:
It is shown that n + k - O(1) comparisons are necessary, on average, to find the kth smallest of n numbers (k l 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.read more
Citations
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Lazy Search Trees
Bryce Sandlund,Sebastian Wild +1 more
TL;DR: The lazy search tree as mentioned in this paper is a comparison-based data structure on the pointer machine that supports order-based operations such as rank, select, membership, predecessor, successor, minimum, and maximum while providing dynamic operations insert, delete, change-key, split, and merge.
An Efficient Approximate Algorithm for the k-th Selection Problem
D. Cantone,G. Cincotti,M. Hofri +2 more
TL;DR: An efficient randomized algorithm for the approximate k-th selection problem that works in-place and it is fast and easy to implement.
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Randomized selection with quintary partitions
TL;DR: It is shown that several versions of Floyd and Rivest’s algorithm Select for finding the kth smallest of n elements require at most n+min{k, n − k}+ o(n) comparisons on average and with high probability.
Book ChapterDOI
Finding a Mediocre Player
TL;DR: In this paper, the authors consider a set of tennis players and their rankings and assume that their ranking is a total order and thus satisfies transitivity and anti-symmetry.
Journal ArticleDOI
Further analysis of the remedian algorithm
Domenico Cantone,Micha Hofri +1 more
TL;DR: An analysis of the remedian, an efficient, known algorithm, for the approximate median selection problem, that is easy to implement, that can be used for data in an array, as well as for streaming data.
References
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Journal ArticleDOI
Time bounds for selection
TL;DR: The number of comparisons required to select the i-th smallest of n numbers is shown to be at most a linear function of n by analysis of a new selection algorithm-PICK.
Journal ArticleDOI
Expected time bounds for selection
Robert W. Floyd,Ronald L. Rivest +1 more
TL;DR: A new selection algorithm is presented which is shown to be very efficient on the average, both theoretically and practically.
Journal ArticleDOI
Algorithm 63: partition
TL;DR: The procedures RANGESUB, RANGEMPY, and RANGEDVD provide for the remaining fundamental operations in range ari thmetic, and real a, b, c, d, e, f is a non-local real procedure.
Journal ArticleDOI
A sorting problem and its complexity
TL;DR: A technique for proving min-max norms of sorting algorithms is given and one new algorithm for finding the minimum and maximum elements of a set with fewest comparisons is proved optimal with this technique.