Yet Another Spatial Indexing Structure

Large data sets of high dimensional objects have become important in applications such as image databases. We present a new hierarchical spatial indexing structure in this paper called the PK-tree, which provides eecient queries, low space overhead and eecient updates. There is a more declarative nature to the deenition of the PK-tree which results in a structure that is unique for a given set of objects to be stored. This in turn enables analysis that is simpler than if the structure were dependent on the order in which points were inserted, deleted, etc. Results for this structure include a bound on the number of children of each node in a PK-tree, a generation algorithm with a worst case complexity of O(N log N) where N is the number of points, and general suucient conditions for the average height of the PK-tree to be O(log N).