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.
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