Thii paper describes the techniques used to optimize relational queries in the SDD-1 distributed database system. Queries are submitted to SDD-1 in a high-level procedural language called Datalan-guage. Optimization begins by translating each Datalanguage query into a relational calculus form called an envelope, which is essentially an aggregate-free QUEL query. This paper is primarily concerned with the optimization of envelopes. Envelopes are processed in two phases. The first phase executes relational operations at various sites of the distributed database in order to delimit a subset of the database that contains all data relevant to the envelope. This subset is called a reduction of the database. The second phase transmits the reduction to one designated site, and the query is executed locally at that site. The critical optimization problem is to perform the reduction phase efficiently. Success depends on designing a good repertoire of operators to use during this phase, and an effective algorithm for deciding which of these operators to use in processing a given envelope against a given database. The principal reduction operator that we employ is called a

A state transition model for the optimization of query processing in a distributed database system is presented. The problem is parametrized by means of a state describing the amount of processing that has been performed at each site where the database is located. A state transition occurs each time a new join or semijoin is executed. Dynamic programming is used to compute recursively the costs of the states and the globally optimal solution, taking into account communication and local processing costs. The state transition model is general enough to account for the possibility of parallel processing among the various sites, as well as for redundancy in the database. The model also permits significant reductions of the necessary computations by taking advantage of simple additivity and site-uniformity properties of a cost model, and of clever strategies that improve on the basic dynamic programming algorithm.

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

The join operation of relational algebra is a cornerstone of relational database systems. Computing the join of several relations is NP-hard in general, whereas special (and typical) cases are tractable. This paper considers joins having an acyclic join graph, for which current methods initially apply a full reducer to efficiently eliminate tuples that will not contribute to the result of the join. From a worst-case perspective, previous algorithms for computing an acyclic join of k fully reduced relations, occupying a total of n ≥ k blocks on disk, use Ω((n + z)k) I/Os,wherez is the size of thejoinresultinblocks. In this paper we show how to compute the join in a time bound that is within a constant factor of the cost of running a full reducer plus sorting the output. For a broad class of acyclic join graphs this is O(sort(n + z)) I/Os, removing the dependence on k from previous bounds. Traditional methods decompose the join into a number of binary joins, which are then carried out one by one. Departing from this approach, our technique is based on computing the size of certain subsets of the result, and using these sizes to compute the location(s) of each data item in the result. Finally, as an initial study of cyclic joins in the I/O model, we show how to compute a join whose join graph is a 3-cycle, in O(n 2 /m +sort(n + z)) I/Os, where m is the number of blocks in internal memory.

Answering queries is computationally very expensive, and many approaches have been proposed in the literature to face this fundamental problem. Some of them are based on optimization modules that exploit quantitative information on the database instance, while other approaches exploit structural properties of the query hypergraph. For instance, acyclic queries can be answered in polynomial time, and also query containment is efficiently decidable for acyclic queries. In this report, we review both quantitative and structural methods for optimizing query answering and identifying tractable classes of queries. Moreover, we provide a formal comparison of structural methods.