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Geometric Search Trees
We describe G-trees, a family of randomized, history-independent search tree data structures. The G-trees encompass several independently-discovered data structures such as zip-trees, zip-zip-trees, and dense skip-trees.
The relatively unknown dense skip-trees(Spiegel & Reynolds Jr, 2009) provide two optimizations: expected node size can be increased by flipping coins of success probabilities k1, and empty vertices are eliminated from the tree. We end this section with a fun observation: if we restrict each nested tree structure in the zipk-trees to store ranks in a single bit (i.e., we cap the geometric distribution at two), we obtain exactly the treaps with k-bit priorities. Bender, Michael A ; Berry, Jonathan W ; Johnson, Rob ; Kroeger, Thomas M ; McCauley, Samuel ; Phillips, Cynthia A ; Simon, Bertrand ; Singh, Shikha ; et al.: Anti-persistence on persistent storage: History-independent sparse tables and dictionaries.
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