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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.

An implicit treap represents a sequence by the inorder traversal of a treap, without storing explicit positional search keys. Each node stores its subtree size. If the left subtree has size $\ell$, the root has local index $\ell$; smaller indices descend left, while larger indices descend right after subtracting $\ell +1$.

An empty tree has size zero; splitting it at zero returns two empty trees. A split at $k$ returns the first $k$ entries and the remainder. If $k\le \ell$, split the left subtree and attach its returned suffix as the root's new left child. Otherwise split the right subtree at $k-\ell -1$ and attach its returned prefix as the root's new right child. Recompute sizes on the return path. A merge assumes that every entry of its first operand precedes every entry of its second; choose the higher-priority root and recursively merge the adjoining inner subtrees.

Both operations preserve inorder traversal order and heap order on priorities. They permit insertion, deletion or moving a contiguous segment through a few splits and merges. Independent identically distributed continuous random priorities give the underlying randomized search-tree balance and expected logarithmic operation cost; a particular tree can still be tall.^[ref]

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.