R-trees arise naturally in the study of groups of isometries of hyperbolic space. An R-tree is a uniquely arcwise connected metric space in which each arc is isometric to a subarc of the reals. It follows that an R-tree is locally arcwise connected, contractible, and one-dimensional. Unique and local arcwise connectivity characterize R-trees among metric spaces. A universal R-tree would be of i...

In this paper, we describe a cost model for an adaptive cellbased index structure which aims at efficient management of immense amounts of spatio-temporal data. We first survey various methods to estimate the performance of R-tree variants. Then, we present our cost model which accurately estimates the number of disk accesses for the adaptive cell-based index structure. To show the accuracy of ...

We propose a scalable technique called Seeded Clustering that allows us to maintain R-tree indices by bulk insertion while keeping pace with high data arrival rates. Our approach uses a seed tree, which is copied from the top k levels of a target R-tree, to classify input data objects into clusters. We then build an Rtree for each of the clusters and insert the input R-trees into the target R-t...

and it is easy to see that this is constant on conjugacy classes. In this setting, it can be shown that η(s) and ζ(s) have extensions as meromorphic functions to the entire complex plane. The proof relies on non-commutative harmonic analysis and the functions are studied via the spectral properties of the Laplace-Beltrami operator. In this note we shall consider an analogous situation where we ...

In this work an R-tree variant, which uses minimum volume covering ellipsoids instead of usual minimum bounding rectangles, is presented. The most significant aspects, which determine R-tree index structure performance, is an amount of dead space coverage and overlaps among the covering regions. Intuitively, ellipsoid as a quadratic surface should cover data more tightly, leading to less dead s...

In the era of huge datasets, the top-k search becomes an effective way to decrease the search time of top-k objects. The original top-k search requires a monotone combination function and lists of objects ordered by attribute values. Our approach of the top-k search is motivated by complex user preferences over product catalogues. Such user preferences are composed of the local user preferences...

In this article, first we generalize the concept of complete parts in hyperrings by introducing the concept R-parts in hyperrings and then we study R-closures in hyperrings. Finally we characterize R-closures in hyperfields.

Let $G$ be a group with identity $e$ and $R$ be a commutative $G$-graded ring with nonzero unity $1$. In this article, we introduce the concept of graded $r$-ideals. A proper graded ideal $P$ of a graded ring $R$ is said to be graded $r$-ideal if whenever $a, bin h(R)$ such that $abin P$ and $Ann(a)={0}$, then $bin P$. We study and investigate the behavior of graded $r$-ideals to introduce ...