Weighted hypertree decompositions and optimal query plans

• Authors: Francesco Scarcello;Gianluigi Greco;Nicola Leone
• Venue: PODS '04 Proceedings of the twenty-third ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
• Year: 2004

Hypertree width [22, 25] is a measure of the degree of cyclicity of hypergraphs. A number of relevant problems from different areas, e.g., the evaluation of conjunctive queries in database theory or the constraint satisfaction in AI, are tractable when their underlying hypergraphs have bounded hypertree width. However, in practical contexts like the evaluation of database queries, we have more information besides the structure of queries. For instance, we know the number of tuples in relations, the selectivity of attributes and so on. In fact, all commercial query-optimizers are based on quantitative methods and do not care about structural properties.In this paper, we define the notion of weighted hypertree decomposition, in order to combine structural decomposition methods with quantitative approaches. Weighted hypertree decompositions are equipped with cost functions, that can be used for modelling many situations where we have further information on the given problem, besides its hypergraph representation. We analyze the complexity of computing the hypertree decompositions having the smallest weights, called minimal hypertree decompositions. We show that, in many cases, adding weights we loose tractability. However, we prove that, under some - not very severe - restrictions on the allowed cost functions and on the target hypertrees, optimal weighted hypertree decompositions can be computed in polynomial time. For some easier hypertree weighting functions, this problem is also highly parallelizable. Then, we provide a cost function that models query evaluation costs and show how to exploit weighted hypertree decompositions for determining (logical) query plans for answering conjunctive queries. Finally, we present the results of an experimental comparison of this query optimization technique with the query optimization of a commercial DBMS. These preliminary results are very promising, as for some large queries (with many joins) our hybrid technique clearly outperforms the commercial optimizer.