Let U be a set of elements and d a distance function defined among them. Let NNk (u) be the k elements in U - {u} having the smallest distance to u. The k-nearest neighbor graph (kNNG) is a weighted directed graph G(U,E) ...

Similarity join is a key operation in metric databases. It retrieves all pairs of elements that are similar. Solving such a problem usually requires comparing every pair of objects of the datasets, even when indexing and ...

A compressed full-text self-index is a data structure that replaces a text and in addition gives indexed access to it, while taking space proportional to the compressed text size. The LZ-index, in particular, requires ...

We introduce a new probabilistic proximity search algorithm for range and K-nearest neighbor (K-NN) searching in both coordinate and metric spaces. Although there exist solutions for these problems, they boil down to a ...

Let X and Y be given Banach spaces, and L(X,Y) be the space of bounded linear operators from X into Y. Compact operators are denoted by K(X,Y). It is shown that under certain conditions if k(X,Y) is an M-ideal of L(X,Y), ...

Let  x,y,z be unit vectors in a Hilbert space, and define the angle θxy by cos θxy  = Re (x,y), 0 ≤ θxy ≤ π.  The object this note  is to give a proof of the following inequality (1)                   θxz   and lt; θxy  + θyz .

The LZ-index is a compressed full-text self-index able to represent a text T-1...u, over an alphabet of size sigma = O(polylog(u)) and with k-th order empirical entropy H-k(T), using 4uH(k)(T) + o(u log sigma) bits for any ...

Proximity searching is the problem of retrieving,from a given database, those objects closest to a query.To avoid exhaustive searching,data structures called indexes are builton the database prior to serving queries.The ...

Let k be the quotient field of a Dedekind domain O, (k ≠ 0) and let G = Spn(k) be the Symplectic Group over k. G acts on the 2n -dimensional vector space V.Let L be a lattice in V, and let Sp(L) be the stabilizer of L in ...