On Random Cartesian Trees

Cartesian trees are binary search trees in which the nodes exhibit the heap property according to a second (priority) key. lithe search key and the priority key are independent, and the tree 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 of ). We indicate how these results can be used in the analysis of divide-and-conquer algorithms for maximal vectors and convex hulls . Finally, we look at distributions for which the expected time per operation grows like n a for a E [112, 1} . © 1994 John Wiley & Sons, Inc .