Compressed Representations of Conjunctive Query Results

Relational queries, and in particular join queries, often generate large output results when executed over a huge dataset. In such cases, it is often infeasible to store the whole materialized output if we plan to reuse it further down a data processing pipeline. Motivated by this problem, we study the construction of space-efficient compressed representations of the output of conjunctive queries, with the goal of supporting the efficient access of the intermediate compressed result for a given access pattern. In particular, we initiate the study of an important tradeoff: minimizing the space necessary to store the compressed result, versus minimizing the answer time and delay for an access request over the result. Our main contribution is a novel parameterized data structure, which can be tuned to trade off space for answer time. The tradeoff allows us to control the space requirement of the data structure precisely, and depends both on the structure of the query and the access pattern. We show how we can use the data structure in conjunction with query decomposition techniques, in order to efficiently represent the outputs for several classes of conjunctive queries.Comment: To appear in PODS'18; 35 pages; comments welcom

Tree Projections and Constraint Optimization Problems: Fixed-Parameter Tractability and Parallel Algorithms

Tree projections provide a unifying framework to deal with most structural decomposition methods of constraint satisfaction problems (CSPs). Within this framework, a CSP instance is decomposed into a number of sub-problems, called views, whose solutions are either already available or can be computed efficiently. The goal is to arrange portions of these views in a tree-like structure, called tree projection, which determines an efficiently solvable CSP instance equivalent to the original one. Deciding whether a tree projection exists is NP-hard. Solution methods have therefore been proposed in the literature that do not require a tree projection to be given, and that either correctly decide whether the given CSP instance is satisfiable, or return that a tree projection actually does not exist. These approaches had not been generalized so far on CSP extensions for optimization problems, where the goal is to compute a solution of maximum value/minimum cost. The paper fills the gap, by exhibiting a fixed-parameter polynomial-time algorithm that either disproves the existence of tree projections or computes an optimal solution, with the parameter being the size of the expression of the objective function to be optimized over all possible solutions (and not the size of the whole constraint formula, used in related works). Tractability results are also established for the problem of returning the best K solutions. Finally, parallel algorithms for such optimization problems are proposed and analyzed. Given that the classes of acyclic hypergraphs, hypergraphs of bounded treewidth, and hypergraphs of bounded generalized hypertree width are all covered as special cases of the tree projection framework, the results in this paper directly apply to these classes. These classes are extensively considered in the CSP setting, as well as in conjunctive database query evaluation and optimization

Guaranteeing the \~O(AGM/OUT) Runtime for Uniform Sampling and OUT Size Estimation over Joins

We propose a new method for estimating the number of answers OUT of a small join query Q in a large database D, and for uniform sampling over joins. Our method is the first to satisfy all the following statements. - Support arbitrary Q, which can be either acyclic or cyclic, and contain binary and non-binary relations. - Guarantee an arbitrary small error with a high probability always in \~O(AGM/OUT) time, where AGM is the AGM bound OUT (an upper bound of OUT), and \~O hides the polylogarithmic factor of input size. We also explain previous join size estimators in a unified framework. All methods including ours rely on certain indexes on relations in D, which take linear time to build offline. Additionally, we extend our method using generalized hypertree decompositions (GHDs) to achieve a lower complexity than \~O(AGM/OUT) when OUT is small, and present optimization techniques for improving estimation efficiency and accuracy.Comment: 19 page

Old Techniques for New Join Algorithms: A Case Study in RDF Processing

Recently there has been significant interest around designing specialized RDF engines, as traditional query processing mechanisms incur orders of magnitude performance gaps on many RDF workloads. At the same time researchers have released new worst-case optimal join algorithms which can be asymptotically better than the join algorithms in traditional engines. In this paper we apply worst-case optimal join algorithms to a standard RDF workload, the LUBM benchmark, for the first time. We do so using two worst-case optimal engines: (1) LogicBlox, a commercial database engine, and (2) EmptyHeaded, our prototype research engine with enhanced worst-case optimal join algorithms. We show that without any added optimizations both LogicBlox and EmptyHeaded outperform two state-of-the-art specialized RDF engines, RDF-3X and TripleBit, by up to 6x on cyclic join queries-the queries where traditional optimizers are suboptimal. On the remaining, less complex queries in the LUBM benchmark, we show that three classic query optimization techniques enable EmptyHeaded to compete with RDF engines, even when there is no asymptotic advantage to the worst-case optimal approach. We validate that our design has merit as EmptyHeaded outperforms MonetDB by three orders of magnitude and LogicBlox by two orders of magnitude, while remaining within an order of magnitude of RDF-3X and TripleBit