Paging binary trees with external balancing

Abstract

We propose the partially paged binary tree principle (PPbin tree principle, for short) for maintaining binary trees which do not fit into core and hence must be (at least partially) paged on secondary storage. The PPbin tree principle can be applied to balanced as well as unbalanced binary trees. Paging a balanced binary tree results in a balanced external binary tree. However, main advantage of the new principle is that even for unbalanced binary trees it is very unlikely that long external access paths will arise. As an example, we describe the partially paged k-d tree which is used as directory in a spatial data structure. The analysis of the expected storage utilization and the expected external height proves the efficiency of the new data structure derived from the application of the PPbin tree principle.