Multiple Quickselect—Hoare's Find algorithm for several elements
Information Processing Letters
An introduction to the analysis of algorithms
An introduction to the analysis of algorithms
Analysis of Hoare's FIND algorithm with median-of-three partition
Random Structures & Algorithms - Special issue: average-case analysis of algorithms
The art of computer programming, volume 3: (2nd ed.) sorting and searching
The art of computer programming, volume 3: (2nd ed.) sorting and searching
Communications of the ACM
Quickselect and the Dickman Function
Combinatorics, Probability and Computing
Comparisons in Hoare's Find Algorithm
Combinatorics, Probability and Computing
Distances and Finger Search in Random Binary Search Trees
SIAM Journal on Computing
On quickselect, partial sorting and multiple quickselect
Information Processing Letters
Note: Moves and displacements of particular elements in Quicksort
Theoretical Computer Science
Adaptive sampling strategies for quickselects
ACM Transactions on Algorithms (TALG)
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Range Quickselect, a simple modification of the well-known Quickselect algorithm for selection, can be used to efficiently find an element with rank k in a given range [i..j], out of n given elements. We study basic cost measures of Range Quickselect by computing exact and asymptotic results for the expected number of passes, comparisons and data moves during the execution of this algorithm. The key element appearing in the analysis of Range Quickselect is a trivariate recurrence that we solve in full generality. The general solution of the recurrence proves to be very useful, as it allows us to tackle several related problems, besides the analysis that originally motivated us. In particular, we have been able to carry out a precise analysis of the expected number of moves of the pth element when selecting the jth smallest element with standard Quickselect, where we are able to give both exact and asymptotic results. Moreover, we can apply our general results to obtain exact and asymptotic results for several parameters in binary search trees, namely the expected number of common ancestors of the nodes with rank i and j, the expected size of the subtree rooted at the least common ancestor of the nodes with rank i and j, and the expected distance between the nodes of ranks i and j.