## On random Cartesian trees (1994)

Venue: | Random Structures Algorithms |

Citations: | 2 - 2 self |

### BibTeX

@ARTICLE{Devroye94onrandom,

author = {Luc Devroye},

title = {On random Cartesian trees},

journal = {Random Structures Algorithms},

year = {1994},

volume = {5},

pages = {305--327}

}

### OpenURL

### Abstract

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}.