7 Acknowledgements Example 6.1 (context Mixed-linear for Pseudo Left-linear Rules)

We thank Shuky Sagiv and H akan Jakobsson for many insightful discussions on cost analysis. Raghu Ramakr-ishnan and Jee Ullman provided valuable comments. The Starburst project at IBM Almaden Research Center and the NAIL! project at Stanford University provided a stimulating environment for this work. References AU79] Alfred Aho and Jeerey D. Ullman. Universal-ity of data retrieval languages. left-and multi-linear rule transformations that maintain context information. restrict computation. Context right-linear (CRL) and right-linear (RL) transformations are ineecient for such overbound queries. We deene overbound queries, and present techniques to optimize over-bound queries. 2. Analytical comparison of the eeciency of context right-linear transformation with magic-sets shows that, in general, the two techniques are incompa-rable. However, for a very useful subclass of stable right-linear programs, CRL performs better than magic-sets. 3. Right-linear and left-linear programs are duals of each other. The rst result identiies a class of queries for which partial sips give better results than full sips. We are able to recognize that there are too many selection conditions , and that we must choose between traversing the graph from source or destination nodes. In case we decide to do the former, we have given algorithms that can perform better than the context right-linear and magic-sets transformations by an order of magnitude. To the best of our knowledge, overbound right-linear is the rst class of programs for which an algorithm using partial sips (CORL) strongly dominates a similar algorithm using full sips (CRL). The idea of using partial sips to gain performance needs to be explored further. For example, the query ?-sg bb is right-linear. It is not overbound right-linear, but could beneet from partial sips. The second result lets us choose CRL over magic-sets for many of the common applications, with conndence that we are not selecting a bad evaluation strategy. We have deened a class of stable programs, and shown that for stable programs on graphs with bounded degree, CRL performs better than magic-sets. We have also learned that for unstable programs (Example 3.2), or for stable programs on graphs with unbounded degree (Example 3.3), CRL can be much worse than magic-sets, and so a choice between CRL and magic-sets depends on the query and the edb characteristics. Our analysis shows that fan-in and fan-out of the database graph are important characteristics. Intuitively, CRL is likely to be better than magic-sets if the fan-in of the database graph going …