It is well known that the performance of quicksort can be improved by selecting the median of a sample of elements as the pivot of each partitioning stage. For large samples the partitions are… (More)

In this paper, we present randomized algorithms over binary search trees such that: (a) the insertion of a set of keys, in any fixed order, into an initially empty tree always produces a random… (More)

Ž . ABSTRACT: In a randomly grown binary search tree BST of size n, any fixed pattern occurs with a frequency that is on average proportional to n. Deviations from the average case are highly… (More)

Hoare’s FIND algorithm can be used to select the jth element out of a file of n elements. It bears a remarkable similarity to Quicksort; in each pass of the algorithm, a pivot element is used to… (More)

Partial match queries arise frequently in the context of large databases, where each record contains a distinct multidimensional key, that is, the key of each record is aK-tuple of values. The… (More)

Quickselect with median-of-3 is largely used in practice and its behavior is fairly well understood. However, the following natural adaptive variant, which we call <i>proportion-from-3</i>, had not… (More)

In this work we present the average-case analysis of orthogonal range search for several multidimensional data structures. We first consider random relaxed K-d trees as a prototypical example. Later… (More)