Average-case complexity for the execution of recursive definitions on relational databases

The execution costs of various types of database queries, expressed in terms of linear recusive definitions, are evaluated for two common query evaluation algorithms in the case where the database relations are represented by forests of labelled oriented trees. In a first stage, the execution costs are computed for a given forest. A key issue in this computation is the partition of the set of nodes in the forest into equivalence classes, the properties of which are explored. Moreover, the representation adopted is conceptually simple and provides additional results which are of interest by themselves. In a second stage, the averages of these costs, computed over all databases representable by forests with a given number of nodes, are also evaluated. Finally, the execution cost of the considered database queries is computed for the case where the underlined database relations are modelled as Hamiltonian digraphs.ou