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Clustering techniques for minimizing external path length
 Proceedings of the International Conference on Very Large Databases
, 1996
"... There are a variety of mainmemory access structures, such as segment trees, and quad trees, whose properties, such as good worstcase behaviour, make them attractive for database applicdions. Unfortunately, the structures are typically ‘long and skinny’, whereas disk data structuies must be ‘short ..."
Abstract

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There are a variety of mainmemory access structures, such as segment trees, and quad trees, whose properties, such as good worstcase behaviour, make them attractive for database applicdions. Unfortunately, the structures are typically ‘long and skinny’, whereas disk data structuies must be ‘shortandfat (that is, have a high fanout and low height) in order to minimize I/O. We consider how to cluster the nodes (that is, map the nodes to disk pages) of mainmemory access structures such that although a path may traverse many nodes, it only traverses a few disk pages. The number of disk pages traversed in a path is called the external path length. We address several versions of the clustering problem. We present a clustering algorithm for tree structures that generates optimal worstcase external path length mappings; we also show how to make it dynamic, to support updates. We extend the algorithm to generate mappings that minimize the average weighted external path lengths. We also show that some other clustering problems, such as finding optimal external path lengths for DAG structures and minimizing
A generalized comparison of quadtree and bintree storage requirements
 Image and Vision Computing
, 1993
"... The quadtree and the bintree data structures are two variants on the principle of hierarchical regular decomposition applied to image representation. A comparison of the storage requirements for images represented by these two methods is presented. The relative storage efficiency of quadand bintrees ..."
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The quadtree and the bintree data structures are two variants on the principle of hierarchical regular decomposition applied to image representation. A comparison of the storage requirements for images represented by these two methods is presented. The relative storage efficiency of quadand bintrees is determined by two factors: the relative node sizes for the two representations as determined by the data structure implementation, and the number of quadtree leaf node pairs that merge to form a single leaf node after conversion to the bintree representation. A probabilistic model for images is developed to analyze the merging probability of quadtree leaf node pairs. The analysis reveals that exactly one half of such pairs are expected to merge. Empirical results closely match these calculations. The resulting storage efficiency for a number of representative implementations is discussed. Each of the data structures has implementations (and associated applications) for which it is more space efficient.