Inherent Complexity of Recursive Queries

AbstractWe give lower bounds on the complexity of certain Datalog queries. Our notion of complexity applies to compile-time optimization techniques for Datalog; thus, our results indicate limitations of these techniques. The main new tool is linear first-order formulas, whose depth (respectively, number of variables) matches the sequential (respectively, parallel) complexity of Datalog programs. We define a combinatorial game (a variant of Ehrenfeucht–Fraı̈ssé games) that can be used to prove nonexpressibility by linear formulas. We thus obtain lower bounds for the sequential and parallel complexity of Datalog queries. We prove syntactically tight versions of our results, by exploiting uniformity and invariance properties of Datalog queries

Updating Recursive XML Views of Relations

This paper investigates the view update problem for XML views published from relational data. We consider XML views defined in terms of mappings directed by possibly recursive DTDs, compressed into DAGs and stored in relations. We provide new techniques to efficiently support XML view updates specified in terms of XPath expressions with recursion and complex filters. The interaction between XPath recursion and DAG compression of XML views makes the analysis of XML view updates rather intriguing. In addition, many issues are still open even for relational view updates, and need to be explored. In response to these, on the XML side, we revise the notion of side effects and update semantics based on the semantics of XML views, and present efficient algorithms to translate XML updates to relational view updates. On the relational side, we propose a mild condition on SPJ views, and show that under this condition the analysis of deletions on relational views becomes PTIME while the insertion analysis is NP-complete. We develop an efficient algorithm to process relational view deletions, and a heuristic algorithm to handle view insertions. Finally, we present an experimental study to verify the effectiveness of our techniques. 1

Linear vs. Polynomial Constraints in Database Query Languages

We prove positive and negative results on the expressive power of the relational calculus augmented with linear constraints. We show non-expressibility of some properties expressed by polynomial constraints. We also show expressibility of some queries involving existence of lines, when the query output has a simple geometrical relation to the input. Finally, we compare the expressive power of linear vs. polynomial constraints in the presence of a discrete order. 1 Introduction An active area of recent research is concerned with integrating constraints into logical formalisms for programming languages [DG,JL87,Ma87,Sa] and database query languages [BJM93,KKR90, Kup90,Kup93,Re90]. Constraints are incorporated in logic programming systems such as CLP, Prolog III and CHIP. The class of linear constraints is of particular interest, because of its applicability and the potential for efficient implementation [HJLL90,JL87,La90]. Kanellakis et.al.[KKR90] describe a methodology to combine const..