Using multiple intervals on space filling curves has a benefit to merely approximating the polygon by a bounding box for indexing purposes. These intervals feature a shapes closer to those of arbitrary, non rectangular polygons. In this paper we examine whether SCUBA (Space filling Curves versus Unsophisticated Bounding box Approximation) is a feasible approach in comparison to a simple boundin...

This paper introduces the notion of space-filling trees, which are analogous to space-filling curves, but have a branching, tree-like structure and are rooted. A space-filling tree is defined by an incremental process that results in a tree for which every point in the space has a finite-length path that converges to it. In contrast to space-filling curves, individual paths in the tree are shor...

Using space-filling curves to order multidimensional data has been found to be useful in a variety of application domains. This paper examines the space-filling curve induced ordering of multidimensional data that has been transformed using shape preserving transformations. It is demonstrated that, although the orderings are not invariant under these transformations, the probability of an order...

In Scientific Computing, space-filling curves are quite commonly used as tools to improve certain properties of data structures or algorithms, or even to provide or simplify algorithmic solutions to particular problems. In the first chapter we will pick out two simple examples – both related to data structures and algorithms on computational grids – to introduce typical data structures and rela...

This paper presents the space-filling curves and their applicability in scheduling, especially in transaction scheduling in Active Real-time Database Systems (ARTDBS). Active real-time databases have emerged as a research area in which concepts of active databases and real-time databases are combined into a real-time database with reactive behaviour. A novel space-filling curve based approach f...

We present a tensor product formulation for Hilbert space-filling curves. Both recursive and iterative formulas are expressed in the paper. We view a Hilbert space-filling curve as a permutation which maps twodimensional n n data elements stored in the row major or column major order to the order of traversing a Hilbert space-filling curve. The tensor product formula of Hilbert space-filling cu...

In Scientific Computing, space-filling curves are quite commonly used as tools to improve certain properties of data structures or algorithms, or even to provide or simplify algorithmic solutions to particular problems. In the first chapter we will pick out two simple examples – both related to data structures and algorithms on computational grids – to introduce typical data structures and rela...

In Scientific Computing, space-filling curves are quite commonly used as tools to improve certain properties of data structures or algorithms, or even to provide or simplify algorithmic solutions to particular problems. In the first chapter we will pick out two simple examples – both related to data structures and algorithms on computational grids – to introduce typical data structures and rela...