Improved Bounds for Finger Search on a RAM

ISB-tree: A new indexing scheme with efficient expected behaviour

“…The class of ( f 1 , f 2 )-smooth distributions (for appropriate choices of f 1 and f 2 ) is a superset of both regular and uniform classes of distributions, as well as of several non-uniform classes [3,14]. Actually, any probability distribution is ( f 1 , Θ(n))-smooth, for a suitable choice of β.…”

“…If the elements are drawn from a smooth distribution, then t = O (1) (with high probability; see [14,25]). The aforementioned choice of functions H(n), R(n) and I(n) ensures that an SIST on n elements, drawn from an (n · g(H(n)), H −1 (H(n) − 1))-smooth distribution μ, can be built in O (n) time and space [14].…”

“…The static interpolation search tree is a searching data structure presented in [14]. It is a static and explicit version of the search trees used in [3,25] that address the classical searching problem, which for our purposes is defined as follows.…”

“…The upper level is a non-straightforward externalization of the static interpolation search tree presented in [14]. The lower level is a forest of buckets, each of which is implemented by a new variant of the classical B-tree, the Lazy B-tree, which we introduce here.…”

“…To overcome these problems, we employ a combinatorial game of bins and balls introduced in [14] that allows to upper bound the number of elements in a bucket, and to approximate an unknown distribution by an almost uniform one.…”