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Path Signatures: A Way to Speed Up Recursion in Relational Databases
June 1996 (vol. 8 no. 3)
pp. 446-454

Abstract—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 here 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 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.

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Index Terms:
Bill-of-materials, clustering, composite objects, path encoding, recursive relations, signatures, transitive closure.
Jukka Teuhola, "Path Signatures: A Way to Speed Up Recursion in Relational Databases," IEEE Transactions on Knowledge and Data Engineering, vol. 8, no. 3, pp. 446-454, June 1996, doi:10.1109/69.506711
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