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Analytical results on the Quadtree storage-requirements
, 1993
"... An analysis of the expected size occupied by a Quadtree is presented. The analysis is based on the general assumption that the storage requirements of internal and external nodes differ. Besides, formulae for the expected number of internal and external nodes at a specific level of the tree are giv ..."
Abstract
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Cited by 4 (2 self)
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An analysis of the expected size occupied by a Quadtree is presented. The analysis is based on the general assumption that the storage requirements of internal and external nodes differ. Besides, formulae for the expected number of internal and external nodes at a specific level of the tree are given. Next, the space efficiency of the most popular Quadtree implementations is examined. Finally, the possible usefulness of these analytical tools in other problems is commented.
Saudi Arabia,
"... It is well known that parallel programming is far more difficult that sequential programming. The need for more abstract programming models where, there is a clear distinction between logical and physical parallelism, is becoming more apparent especially with the advent of large scale and high perfo ..."
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Cited by 1 (0 self)
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It is well known that parallel programming is far more difficult that sequential programming. The need for more abstract programming models where, there is a clear distinction between logical and physical parallelism, is becoming more apparent especially with the advent of large scale and high performance computing. In this context, the Gamma formalism was proved to be a suitable tool that separates the problem definition from its implementation leaving for later stages the perception of the imperative paradigm. In this paper, we developed a specification for a virtual Gamma machine to be used as an abstract platform for the parallel programming without any consideration of the physical hardware. As an application of the virtual Gamma machine, we developed a parallel algorithm for the quadtree spatial data structure. The obtained experimental results showed the ease and convenience of developing gamma-based programs in addition to the almost linear speedup. Keywords: Parallel processing; high-level programming paradigms, Gamma; Multiset transformation; performance evaluation; quadtree spatial data structures; image decomposition. 1-
Particle simulations
"... a has moke ues is f par g the tate imula Other spatial data structures can be used as alternatives to uniform grids, such as hierarchical data structures including quadtrees and octrees. As a matter of interest, to represent the 2D simulation space, quadtrees offer adaptive space decom-position. Eve ..."
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a has moke ues is f par g the tate imula Other spatial data structures can be used as alternatives to uniform grids, such as hierarchical data structures including quadtrees and octrees. As a matter of interest, to represent the 2D simulation space, quadtrees offer adaptive space decom-position. Every cell in a quadtree is square shaped and, can be decomposed into its four quadrants if necessary. This regular decomposition has the advantage of easy implementation. A sample quadtree containing a number of particles can be seen in
ML-Quadtree: The Design of an Efficient Access Method for Spatial Database Systems
, 2003
"... Abstract. The aim of this paper is to present a new indexing technique that provides an efficient support for retrieving and handling spatial data. Traditionally, the mapping between layers (in a thematic point of view) and index structures is one to one. Each layer is associated with an index struc ..."
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Abstract. The aim of this paper is to present a new indexing technique that provides an efficient support for retrieving and handling spatial data. Traditionally, the mapping between layers (in a thematic point of view) and index structures is one to one. Each layer is associated with an index structure. In some previous work, we have presented a data structure, the FI-Quadtree that handles a set of images using only one index structure. This handling is a raster-oriented format. In this paper, we focus on the processing of these objects from the vector oriented format point of view. The Multi-Layer Quadtree (ML-Quadtree) is a new data structure that allows the storage and processing of several layers at the same time. This structure is based on the PM-Quadtree, which allows the storage of only a single-layer map. The aim of the ML-Quadtree is to be able to manage, store and perform queries among multiple layers simultaneously. The design and the manipulation of the proposed structure is presented in this paper whereas the implementation and the experimentation result will be treated in a subsequent paper. 1.
