In this article, we study the k-clustering query problem on road networks, an important problem in Geographic Information Systems. Using Euclidean embeddings and reduction to fast nearest neighbor search, we devise approximation algorithms for these problems. Since these problems are difficult to solve exactly – and even hard to approximate for most variants – we compare our constant factor app...

In the present paper we use the Wannier function basis to construct lattice approximations of the nonlinear Schrödinger equation with a periodic potential. We show that the nonlinear Schrödinger equation with a periodic potential is equivalent to a vector lattice with long-range interactions. For the case-example of the cosine potential we study the validity of the so-called tight-binding appro...

This paper concerns approximate nearest neighbor searching algorithms, which have become increasingly important, especially in high dimensional perception areas such as computer vision, with dozens of publications in recent years. Much of this enthusiasm is due to a successful new approximate nearest neighbor approach called Locality Sensitive Hashing (LSH). In this paper we ask the question: c...

All van Hove singularities in the density of states (DOS) face-centered cubic lattice nearest and next-nearest neighbour approximation, focusing on higher-order ones, are found classified. At special values ratio $\tau$ hopping integrals, $t$ $t'$, giant DOS singularities, caused by lines or surfaces, formed. An exact formula for which provides efficient numerical implementation is proposed. Th...

We propose a novel approach to solving the approximate k-nearest neighbor search problem in metric spaces. The search structure is based on a navigable small world graph with vertices corresponding to the stored elements, edges to links between them, and a variation of greedy algorithm for searching. The navigable small world is created simply by keeping old Delaunay graph approximation links p...

Providing a fast and accurate (exact or approximate) access to large-scale multidimensional data is a ubiquitous problem and dates back to the early days of large-scale Information Systems. Similarity search, requiring to resolve nearest neighbor (NN) searches, is a fundamental tool for structuring information space. Permutation-based Indexing (PBI) is a reference-based indexing scheme that acc...

For object recognition based on nearest neighbor search of local descriptors such as SIFT, it is important to keep the nearest neighbor search efficient to deal with a huge number of descriptors. In this report we propose a new method of efficient recognition based on the observation that the level of accuracy of nearest neighbor search for correct recognition depends on images to be recognized...

For object recognition based on nearest neighbor search of local descriptors such as SIFT, it is important to make the nearest neighbor search efficient to deal with a huge number of descriptors. In this report we propose a new method of efficient recognition based on the observation that the level of accuracy of nearest neighbor search for correct recognition depends on images to be recognized...

We studied theoretically the effect of a low concentration adsorbed polar molecules on optical conductivity graphene, within Kubo linear response approximation. Our analysis is based continuum model approximation that includes up to next-to-nearest neighbors in pristine graphene effective Hamiltonian. results show can be expressed terms renormalized quasiparticle parameters ${\stackrel{\ifmmode...