B-Treaps Revised: Write Efficient Randomized Block Search Trees with High Load
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Uniquely represented data structures represent each logical state with a unique storage state. We study the problem of maintaining a dynamic set of n keys from a totally ordered universe in this context. We introduce a two-layer data structure called (α,ε)-Randomized Block Search Tree (RBST) that is uniquely represented and suitable for external memory. Though RBSTs naturally generalize the well-known binary Treaps, several new ideas are needed to analyze the expected search, update, and storage, efficiency in terms of block-reads, block-writes, and blocks stored. We prove that searches have O(ε^-1 + log_α n) block-reads, that (α, ε)-RBSTs have an asymptotic load-factor of at least (1-ε) for every ε∈ (0,1/2], and that dynamic updates perform O(ε^-1 + log_α(n)/α) block-writes, i.e. O(1/ε) writes if α=Ω(log n/loglog n ). Thus (α, ε)-RBSTs provide improved search, storage-, and write-efficiency bounds in regard to the known, uniquely represented B-Treap [Golovin; ICALP'09].
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