Abstract

There are a variety of main-memory access structures, such as segment trees, and quad trees, whose properties, such as good worst-case behaviour, make them attractive for database applicdions. Unfortunately, the structures are typically ‘long and skinny’, whereas disk data structuies must be ‘short-and-fat (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 main-memory access structures such that although a path may traverse many nodes, it only tra-verses a few disk pages. The number of disk pages traversed in a path is called the exter-nal path length. We address several versions of the clustering problem. We present a clus-tering algorithm for tree structures that gener-ates optimal worst-case external path length mappings; we also show how to make it dy-namic, to support updates. We extend the al-gorithm to generate mappings that minimize the average weighted external path lengths. We also show that some other clustering prob-lems, such as finding optimal external path lengths for DAG structures and minimizing

Citations