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Cecilia R. Aragon coauthored the randomized search-tree construction with Raimund Seidel. Their treap combines binary search tree order on keys with heap order on random priorities. A key set and distinct priorities determine the tree; independent random priorities give expected logarithmic search and update costs. The analysis separates expected cost from the possibly linear height of a particular realization.^[ref]

The construction makes balancing probabilistic without storing the explicit balance conditions used by AVL trees. Operations that split or join a tree preserve the two orderings, making the idea useful for both ordered dictionaries and sequence data structures.

Raimund Seidel coauthored Randomized Search Trees by Raimund Seidel and Cecilia R. Aragon with Cecilia R. Aragon. The paper analyzes search trees whose shape is governed by random priorities. Combining binary search tree order and heap order gives the treap, supporting searches, updates and split/join operations with expected bounds.^[ref]

The key idea is to analyze the distribution of the whole tree instead of enforcing a fixed local balance ratio after every update. For example, the item with highest priority becomes the root, and the same construction applies recursively to the smaller and larger keys. This turns priority independence into an analyzable balancing mechanism.

By Raimund Seidel, Cecilia R. Aragon.

Primary source: faculty.washington.edu/aragon/pubs/rst96.pdf

Section 2, treap invariants and split/join; later sections analyze expected depth and operation cost.