In geometric range searching, algorithmic problems of the following type are considered.
Given an n-point set P in the plane, build a data structure so that, given a query triangle R …

The nearest neighbor problem is the follolving: Given a set of n points P=(PI,..., p,} in some
metric space X, preprocess P so as to efficiently answer queries which require finding bhe …

Consider a set of S of n data points in real d-dimensional space, Rd, where distances are
measured using any Minkowski metric. In nearest neighbor searching, we preprocess S into …

Current state-of-the-art approximate nearest neighbor search (ANNS) algorithms generate
indices that must be stored in main memory for fast high-recall search. This makes them …

We introduce a new low-distortion embedding of \ell_2^d into \ell_p^O(\logn) (p=1,2) called
the fast Johnson–Lindenstrauss transform (FJLT). The FJLT is faster than standard random …

Regression and classification methods based on similarity of the input to stored examples
have been part of the arsenal in statistics and computer science for decades. Despite …

We introduce a new low-distortion embedding of l2d into lpO (log n)(p= 1, 2), called the Fast-
Johnson-Linden-strauss-Transform. The FJLT is faster than standard random projections …

We address the problem of designing data structures that allow efficient search for
approximate nearest neighbors. More specifically, given a database consisting of a set of …

The nearest neighbor problem is defined as follows: Given a set P of n points in some metric
space (X, D), build a data structure that, given any point q, returns a point in P that is closest …

A typical range-searching problem has the following form: Pre-process a set S of points in R*
so that the points of S lying inside a query region can be reported or counted quickly. We …