The development of a spatiotemporal access method suitable for objects moving on fixed networks is a very attractive challenge due to the great number of real-world spatiotemporal database applications and fleet management systems dealing with this type of objects. In this work, a new indexing technique, named Fixed Network R-Tree (FNR-Tree), is proposed for objects constrained to move on fixed...

We prove an acylindrical accessibility theorem for finitely generated groups acting on R-trees. Namely, we show that if G is a freely indecomposable non-cyclic k-generated group acting minimally and M-acylindrically on an R-tree X then for any ǫ > 0 there is a finite subtree Yǫ ⊆ X of measure at most 2M (k − 1) + ǫ such that GYǫ = X. This generalizes theorems of Z.Sela and T.Delzant about actio...

Several applications require management of data which is spatially dynamic, e.g., tracking of battle ships or moving cells in a blood sample. The capability of handling the temporal aspect, i.e., the history of such type of data, is also important. This paper presents and evaluates three temporal extensions of the R-tree, the 3D R-tree, the 2+3 R-tree and the HR-tree, which are capable of index...

Driven by many real applications, in this paper we study the problem of similarity search with implicit object features; that is, the features of each object are not pre-computed/evaluated. As the existing similarity search techniques are not applicable, a novel and efficient algorithm is developed in this paper to approach the problem. The R-tree based algorithm consists of two steps: feature ...

The construction of an efficient tree structure should take into account parameters which can be optimised. Coverage of a node, "dead area" of a node and overlap between nodes are examples of such parameters. Taking these parameters under account is important since minimization of a node coverage leads to more precise searching within the tree, minimization of a node "dead area" reduces the num...

The high data availability and the increasing number of GIS users have motivated the emergence of distributed algorithms to process spatial operations efficiently. They are based on distributed indexes for an high performance processing. Researches and ongoing work use R-trees as a distributed spatial structure for indexing and retrieval of geo objects. However, these indexes have shown a chall...

Motivated by the work of Leininger on hyperbolic equivalence of homotopy classes of closed curves on surfaces, we investigate a similar phenomenon for free groups. Namely, we study the situation when two elements g, h in a free group F have the property that for every free isometric action of F on an R-tree X the translation lengths of g and h on X are equal.

In a visualization system, one of the key issues is to optimize performance and visual fidelity. This is especially critical for large virtual environments where the models do not fit into the memory. In this paper, we present a novel structure called HDoV-tree that can be tuned to provide excellent visual fidelity and performance based on the degree of visibility of objects. HDoV-tree also exp...