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<p><b>Abstract</b>—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.</p>
Bill-of-materials, clustering, composite objects, path encoding, recursive relations, signatures, transitive closure.

J. Teuhola, "Path Signatures: A Way to Speed Up Recursion in Relational Databases," in IEEE Transactions on Knowledge & Data Engineering, vol. 8, no. , pp. 446-454, 1996.
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