Controlling the Search in Bottom - Up

Bottom-up evaluation of queries on deductive databases has many advantages over an evaluation scheme such as Prolog. It is sound and complete with respect to the declarative semantics of least Herbrand models for positive Horn clause programs. In particular, it is able to avoid innnite loops by detecting repeated (possibly cyclic) subgoals. Further, in many database applications , it is more eecient than Prolog due to its set-orientedness. However , the completely set-oriented, breadth-rst search strategy of bottom-up evaluation has certain disadvantages. For example, to evaluate several classes of programs with negation (or aggregation), it is necessary to order the inferences; in essence, we must evaluate all answers to a negative sub-goal before making an inference that depends upon the negative subgoal. A completely breadth-rst search strategy ((14]) would have to maintain a lot of redundant subgoal dependency information to achieve this. We present a technique to order the use of generated subgoals, that is a hybrid between pure breadth-rst and pure depth-rst search. The technique , called Ordered Search, is able to maintain subgoal dependency information eeciently, while being able to detect repeated subgoals, and avoid innnite loops. Also, the technique avoids repeated computation and is complete for DATALOG. We demonstrate the power of Ordered Search through two applications. First, we show that it can be used to evaluate programs with left-to-right modularly stratiied negation and aggregation more ee-ciently than with any previously known bottom-up technique. Second, we illustrate its use for optimizing single-answer queries for linear programs.