Decoupling partitioning and grouping

Abstract

The principle of decoupling the partitioning and grouping processes that form the basis of most spatial indexing methods that use tree directories of buckets is explored. The decoupling is designed to overcome the following drawbacks of traditional solutions:(1) multiple postings in disjoint space decomposition methods that lead to balanced trees such as the hB-tree where a node split in the event of node overflow may be such that one of the children of the node that was split becomes a child of both of the nodes resulting from the split;(2) multiple coverage and nondisjointness of methods based on object hierarchies such as the R-tree which lead to nonunique search paths;(3) directory nodes with similarly-shaped hyper-rectangle bounding boxes with minimum occupancy in disjoint space decomposition methods such as those based on quadtrees and k-d trees that make use of regular decomposition.The first two drawbacks are shown to be overcome by the BV-tree where as a result of decoupling the partitioning and grouping processes, the union of the regions associated with the nodes at a given level of the directory does not necessarily contain all of the data points although all searches take the same amount of time. The BV-tree is not plagued by the third drawback. The third drawback is shown to be overcome by the PK-tree where the grouping process is based on ensuring that every node has at least k objects or blocks. The PK-tree is not plagued by the first two drawbacks as they are inapplicable to it. In both cases, the downside of decoupling the partitioning and grouping processes is that the resulting structure is not necessarily balanced, although, since the nodes have a relatively large fanout, the deviation from a balanced structure is relatively small.