On the bottom - up evaluation of recursive queries

In this paper, we present an optimal bottom-up evaluation method for handling both linear and non-linear recursion. Based on the well-known magic-set method, we develop a technique: labelling to record the cyclic paths during the execution of the first phase of the magic-set method and suspending the computation for the cyclic data in the second phase to avoid the redundant evaluation. Then we postpone this computation to an iteration process (the third phase) which evaluates the remaining answers only along each cyclic path. In this way, we can guarantee the completeness. In addition, for a large class of programs we further optimize our method by elaborating the iteration process and generating most answers for each cyclic path directly from the intermediate results instead of evaluating them by performing algebraic operations (after some of answers for the first cyclic path are produced). Because the cost of generating an answer is much less than that of evaluating an answer, this optimization is significant.