A graph-theoretic approach to map conceptual designs to XML schemas

We propose a mapping from a database conceptual design to a schema for XML that produces highly connected and nested XML structures. We first introduce two alternative definitions of the mapping, one modeling entities as global XML elements and expressing relationships among them in terms of keys and key references (flat design), the other one encoding relationships by properly including the elements for some entities into the elements for other entities (nest design). Then we provide a benchmark evaluation of the two solutions showing that the nest approach, compared to the flat one, leads to improvements in both query and validation performances. This motivates us to systematically investigate the best way to nest XML structures. We identify two different nesting solutions: a maximum depth nesting, that keeps low the number of costly join operations that are necessary to reconstruct information at query time using the mapped schema, and a maximum density nesting, that minimizes the number of schema constraints used in the mapping of the conceptual schema, thus reducing the validation overhead. On the one hand, the problem of finding a maximum depth nesting turns out to be NP-complete and, moreover, it admits no constant ratio approximation algorithm. On the other hand, we devise a graph-theoretic algorithm, NiduX, that solves the maximum density problem in linear time. Interestingly, NiduX finds the optimal solution for the harder maximum depth problem whenever the conceptual design graph is either acyclic or complete. In randomly generated intermediate cases of the graph topology, we experimentally show that NiduX finds a good approximation of the optimal solution.