An efficient relational implementation of recursive relationships using path signatures

The `parts explosion´ is a classical problem, which is hard for relational database systems, due to recursion. A simple solution is suggested, which packs information of an ancestor path of a tuple into a fixed-length code, called signature. The coding technique is carefully adjusted to enable an efficient retrieval of the transitive closure, in terms of both disk accesses and DBMS calls. The code is lossy, and its purpose is to define a reasonably small superset of the closure, as well as establish an effective order of clustering. The method performs best for tree-structured hierarchies, where the processing time typically decreases by a factor of more than ten, compared to the trivial method. Also general directed graphs, both acyclic and cyclic, can be handled more efficiently