Existing encoding schemes and index structures proposed for XML query processing primarily target the containment relationship, specifically the parent–child and ancestor–descendant relationship. The presence of preceding-sibling and following-sibling location steps in the XPath specification, which is the de facto query language for XML, makes the horizontal navigation, besides the vertical na...

We propose a new algorithm to solve the problem of joining two spatial relations R and S when S is indexed by an R-tree. The method combines classical query processing techniques and a plane-sweeping algorithm. We compare our approach to the simple indexed-nested-loop method and to the state-of-the-art algorithms, and show through analysis and experiments on synthetic and real-life datasets tha...

The ever-increasing of spatial datasets and the widely application of the complex computation have motivated the emergence of distributed algorithms to process spatial operations efficiently. The R-tree index is broadly used by researches as a distributed spatial structure for indexing and retrieval of spatial objects. However, a big challenge has arisen, that is, how to check the consistency o...

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...

A very important class of spatial queries consists of nearestneighbor (NN) query and its variations. Many studies in the past decade utilize R-trees as their underlying index structures to address NN queries efficiently. The general approach is to use R-tree in two phases. First, R-tree’s hierarchical structure is used to quickly arrive to the neighborhood of the result set. Second, the R-tree ...

A filling subgroup of a finitely generated free group F (X) is a subgroup which does not fix a point in any very small action free action on an R-tree. For the free group of rank two, we construct a combinatorial algorithm to determine whether or not a given finitely generated subgroup is filling. In higher ranks, we discuss two types of non-filling subgroups: those contained in loop vertex sub...

Since its introduction in 1984, R-tree has been proven to be one of the most practical and well-behaved data structures for accommodating dynamic massive sets of geometric objects and conducting a very diverse set of queries on such datasets in real-world applications. This success has led to a variety of versions, each one trying to tune the performance parameters of the original proposal. Amo...