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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Proceedings ArticleDOI
Minimizing randomness in minimum spanning tree, parallel connectivity, and set maxima algorithms
Seth Pettie,Vijaya Ramachandran +1 more
TL;DR: This work considers the problem of selection and proposes new algorithms for these problems which preserve optimality while saving an exponential number of random bits, in the case of computing minimum spanning trees and MST/SSSP sensitivity analysis.
Proceedings ArticleDOI
Selecting the median
Dorit Dor,Uri Zwick +1 more
TL;DR: It is shown that the median of a set containing n elements can always be found using at most at most $c \cdot n$ comparisons, where c<2.95.
Journal ArticleDOI
On Floyd and Rivest's SELECT algorithm
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.
Journal ArticleDOI
Adaptive sampling strategies for quickselects
TL;DR: The results strongly suggest that a suitable implementation of ν-find could be the method of choice in a practical setting and show that proportion-from-s-like strategies are optimal when s→∞.
Proceedings ArticleDOI
Median selection requires (2+/spl epsiv/)n comparisons
Dorit Dor,U. Zwick +1 more
TL;DR: A (2+/spl epsiv/)n lower bound is obtained on the number of comparisons required, in the worst case, for selecting the median of n elements using a weight function that allows us to combine leaf counting and adversary arguments.
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.