From continua to R-trees

We show how to associate an R-tree to the set of cut points of a continuum. If X is a continuum without cut points we show how to associate an R-tree to the set of cut pairs of X.Comment: This is the version published by Algebraic & Geometric Topology on 1 November 200

Non-unique ergodicity, observers' topology and the dual algebraic lamination for R\R-trees

We continue in this article the study of laminations dual to very small actions of a free group F on R-trees. We prove that this lamination determines completely the combinatorial structure of the R-tree (the so-called observers' topology). On the contrary the metric is not determined by the lamination, and an R-tree may be equipped with different metrics which have the same observers' topology.Comment: to appear in the Illinois Journal of Mat

Optimizing Spatial Databases

This paper describes the best way to improve the optimization of spatial databases: through spatial indexes. The most commune and utilized spatial indexes are R-tree and Quadtree and they are presented, analyzed and compared in this paper. Also there are given a few examples of queries that run in Oracle Spatial and are being supported by an R-tree spatial index. Spatial databases offer special features that can be very helpful when needing to represent such data. But in terms of storage and time costs, spatial data can require a lot of resources. This is why optimizing the database is one of the most important aspects when working with large volumes of data.Spatial Database, Spatial Index, R-tree, Quadtree, Optimization