ΔB+ tree: indexing 3D point sets for pattern discovery

Three-dimensional point sets can be used to represent data in different domains. Given a database of 3D point sets, pattern discovery looks for similar subsets that occur in multiple point sets. Geometric hashing has proved to be an effective technique in discovering patterns in 3D point sets. However, the method are has shortcomings. We propose a new indexing technique called ΔB⁺ trees. It is an extension of B⁺-trees that stores point triplet information and overcomes shortcomings of the geometric hashing technique. We introduce four different ways of constructing the key from a triplet. We give an analytical comparison between the new index structure and the geometric hashing technique. We also conduct experiments on both synthetic data and real data to evaluate performance.