Tree-database design criteria and equivalent decompositions

Determine how to construct, from a set of trees representing an application, an equivalent set of trees satisfying specified design criteria, and identify appropriate criteria for evaluating such tree-database designs.

Background

A tree database may represent an application using either many small trees or fewer larger trees. The tree algebra supports decomposition of large trees and composition of smaller trees, making alternative database organizations possible.

The paper leaves unresolved both the procedure for finding an equivalent tree set satisfying prescribed criteria and the criteria themselves. It mentions lossless decomposition in relational database design as an example of a possible criterion.

References

Hence the question: given a set of trees representing an application how can one find an 'equivalent' set of trees satisfying a set criteria? To this end one would obviously need to use the tree algebra which allows to decompose large trees to smaller trees or to compose small trees to create larger ones. Of equal importance is the question: what criteria should one use? (e.g. one criterion used in the relational database design is that of `lossless decomposition').

— Tree Databases  (2609.03538 - Spyratos, 3 Sep 2026) in Section 8, “Concluding remarks and perspectives,” research line “Tree database design”