Towards Optimal Multiple Selection
نویسندگان
چکیده
The multiple selection problem asks for the elements of rank r1, r2, . . . , rk from a linearly ordered set of n elements. Let B denote the information theoretic lower bound on the number of element comparisons needed for multiple selection. We first show that a variant of multiple quickselect — a well known, simple, and practical generalization of quicksort — solves this problem with B + O(n) expected comparisons. We then develop a deterministic divide-and-conquer algorithm that solves the problem in O(B) time and B + o(B) + O(n) element comparisons.
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