New Algorithms for Selection

Abstract New algorithms are presented to select the k largest elements, and give their respective order, of a totally ordered set of n elements, when k is small compared to n . The performance of these algorithms improves over that of previously known algorithms. One of these algorithms is optimal for a wide range of values of n and k . The algorithms can be modified to select the k th largest element only. The performance of the modified algorithms improves, for asymptotic values of n , over that of previously known algorithms for selecting the k th largest element.