B-Treaps: A uniquely represented alternative to B-trees

Abstract

We present the first uniquely represented data structure for an external memory model of computation, a B-tree analogue called a B-treap. Uniquely represented data structures represent each logical state with a unique machine state. Such data structures are strongly history-independent; they reveal no information about the historical sequence of operations that led to the current logical state. For example, a uniquely represented file-system would support the deletion of a file in a way that, in a strong information-theoretic sense, provably removes all evidence that the file ever existed. Like the B-tree, the B-treap has depth , uses linear space with high probability, where is the block transfer size of the external memory, and supports efficient one-dimensional range queries. © 2009 Springer Berlin Heidelberg.