Efficient handling of SPARQL OPTIONAL for OBDA

OPTIONAL is a key feature in SPARQL for dealing with missing information. While this operator is used extensively, it is also known for its complexity, which can make efficient evaluation of queries with OPTIONAL challenging. We tackle this problem in the Ontology-Based Data Access (OBDA) setting, where the data is stored in a SQL relational database and exposed as a virtual RDF graph by means of an R2RML mapping. We start with a succinct translation of a SPARQL fragment into SQL. It fully respects bag semantics and three-valued logic and relies on the extensive use of the LEFT JOIN operator and COALESCE function. We then propose optimisation techniques for reducing the size and improving the structure of generated SQL queries. Our optimisations capture interactions between JOIN, LEFT JOIN, COALESCE and integrity constraints such as attribute nullability, uniqueness and foreign key constraints. Finally, we empirically verify effectiveness of our techniques on the BSBM OBDA benchmark

The Effect of Cost Distributions on Evolutionary Optimization Algorithms

According to the No-Free-Lunch theorems of Wolpert and Macready, we cannot expect one generic optimization technique to outperform others on average [WM97]. For every optimization technique there exist \easy" and \hard" problems. However, only little is known as to what criteria determine the particular diculty of a problem. In this paper, we address this question from an evolutionary computing point of view. We use cost distributions, i.e., the frequencies of the objective function's values occurring in the search spaces, to devise a classication of optimization problems. We scrutinize the inuence of cost distributions on the single algorithmic components of evolutionary computing. Our analysis helps identifying (1) problems where evolutionary algorithms are overhead, (2) problems where evolutionary algorithms are highly suitable optimization algorithms, as well as (3) problems that pose diculties for evolutionary techniques

Duplicate-free Generation of Alternatives in Transformation-based Optimizers

Transformation-based optimizers that explore a search space exhaustively usually apply all possible transformation rules on each alternative, and stop when no new information is produced. In general, different sequences of transformation rules may end up deriving the same element. The optimizer must detect and discard these duplicate elements generated by multiple paths. In this paper we consider two questions: How bad is the overhead of duplicate generation? And then, how can it be avoided? We use a restricted class of join reordering to illustrate the problem. For the first question, our analysis shows that as queries get larger, the number of duplicates is several times that of the new elements. And even for small queries, duplicates are generated more often than new elements. For the second question, we describe a technique to avoid generating duplicates, based on keeping track of (a summary of) the derivation history of each element. Keywords Query optimization, Transformationbas..

Uniformly-Distributed Random Generation of Join Orders

. In this paper we study the space of operator trees that can be used to answer a join query, with the goal of generating elements form this space at random. We solve the problem for queries with acyclic query graphs. We first count, in O(n 3 ) time, the exact number of trees that can be used to evaluate a given query on n relations. The intermediate results of the counting procedure then serve to generate random, uniformly distributed operator trees in O(n 2 ) time per tree. We also establish a mapping between the N operator trees for a query and the integers 1 through N ---i. e. a ranking--- and describe ranking and unranking procedures with complexity O(n 2 ) and O(n 2 log n), respectively. 1 Introduction 1.1 Background The selection of a join evaluation order is a major task of relational query optimizers [Ull82, CP85, KRB85]. The problem can be stated as that of finding an operator tree to evaluate a given query, so that the estimated evaluation cost is minimum. In pract..