Path signatures: a way to speed up recursion in relational databases

Composite objects often involve recursive relationships, so-called bills-of-materials, which are cumbersome to handle in relational database systems. The relationships constitute a directed graph, where the successors of a node represent its components, recursively. Instead of the whole transitive closure (all ancestor-descendant pairs), the task is to retrieve the descendants of any given node. A simple relational solution is suggested, which packs information of the ancestor path of each node into a fixed-length code, called the signature. The code is nonunique, and its purpose is to define a relatively small superset of the descendants, as well as to establish a basis for clustering. It supports effective retrieval of the descendants, in terms of both disk accesses and DBMS calls. The method performs best for tree-structured graphs, where the processing time typically decreases by a factor of more than 10, compared to a simple loop of joins. Also, general directed graphs, both acyclic and cyclic, can be processed more effectively. The method is implemented on top of a relational system, but advantages can be gained on other platforms, too