On random cartesian trees

Abstract

AbstractCartesian trees are binary search trees in which the nodes exhibit the heap property according to a second (priority) key. If the search key and the priority key are independent, and the trees is built based on n independent copies, Cartesian trees basically behave like ordinary random binary search trees. In this article, we analyze the expected behavior when the keys are dependent: in most cases, the expected search, insertion, and deletion times are Φ(√n). We indicate how these results can be used in the analysis of divide‐and‐conguer algorithms for maximal vectors and convex hulls. Finally, we look at distributions for which the expected time per operation grows like na for a ϵ[1/2, 1]. © 1994 John Wiley & Sons, Inc.