Matteo Riondato

Learning-based Query Performance Modeling and Prediction

Accurate query performance prediction (QPP) is central to effective resource management, query optimization and query scheduling. Analytical cost models, used in current generation of query optimizers, have been successful in comparing the costs of alternative query plans, but they are poor predictors of execution latency. As a more promising approach to QPP, this paper studies the practicality and utility of sophisticated learning-based models, which have recently been applied to a variety of predictive tasks with great success, in both static (i.e., fixed) and dynamic query workloads. We propose and evaluate predictive modeling techniques that learn query execution behavior at different granularities, ranging from coarse-grained plan-level models to fine-grained operator-level models. We demonstrate that these two extremes offer a tradeoff between high accuracy for static workload queries and generality to unforeseen queries in dynamic workloads, respectively, and introduce a hybrid approach that combines their respective strengths by selectively composing them in the process of QPP. We discuss how we can use a training workload to (i) pre-build and materialize such models offline, so that they are readily available for future predictions, and (ii) build new models online as new predictions are needed. All prediction models are built using only static features (available prior to query execution) and the performance values obtained from the offline execution of the training workload. We fully implemented all these techniques and extensions on top of Postgre SQL and evaluated them experimentally by quantifying their effectiveness over analytical workloads, represented by well-established TPC-H data and queries. The results provide quantitative evidence that learning-based modeling for QPP is both feasible and effective for both static and dynamic workload scenarios.

PARMA: a parallel randomized algorithm for approximate association rules mining in MapReduce

Frequent Itemsets and Association Rules Mining (FIM) is a key task in knowledge discovery from data. As the dataset grows, the cost of solving this task is dominated by the component that depends on the number of transactions in the dataset. We address this issue by proposing PARMA, a parallel algorithm for the MapReduce framework, which scales well with the size of the dataset (as number of transactions) while minimizing data replication and communication cost. PARMA cuts down the dataset-size-dependent part of the cost by using a random sampling approach to FIM. Each machine mines a small random sample of the dataset, of size independent from the dataset size. The results from each machine are then filtered and aggregated to produce a single output collection. The output will be a very close approximation of the collection of Frequent Itemsets (FIs) or Association Rules (ARs) with their frequencies and confidence levels. The quality of the output is probabilistically guaranteed by our analysis to be within the user-specified accuracy and error probability parameters. The sizes of the random samples are independent from the size of the dataset, as is the number of samples. They depend on the user-chosen accuracy and error probability parameters and on the parallel computational model. We implemented PARMA in Hadoop MapReduce and show experimentally that it runs faster than previously introduced FIM algorithms for the same platform, while 1) scaling almost linearly, and 2) offering even higher accuracy and confidence than what is guaranteed by the analysis.

Space-round tradeoffs for MapReduce computations

This work explores fundamental modeling and algorithmic issues arising in the well-established MapReduce framework. First, we formally specify a computational model for MapReduce which captures the functional flavor of the paradigm by allowing for a flexible use of parallelism. Indeed, the model diverges from a traditional processor-centric view by featuring parameters which embody only global and local memory constraints, thus favoring a more data-centric view. Second, we apply the model to the fundamental computation task of matrix multiplication presenting upper and lower bounds for both dense and sparse matrix multiplication, which highlight interesting tradeoffs between space and round complexity. Finally, building on the matrix multiplication results, we derive further space-round tradeoffs on matrix inversion and matching.

Mining top-K frequent itemsets through progressive sampling

We study the use of sampling for efficiently mining the top-K frequent itemsets of cardinality at most w. To this purpose, we define an approximation to the top-K frequent itemsets to be a family of itemsets which includes (resp., excludes) all very frequent (resp., very infrequent) itemsets, together with an estimate of these itemsets’ frequencies with a bounded error. Our first result is an upper bound on the sample size which guarantees that the top-K frequent itemsets mined from a random sample of that size approximate the actual top-K frequent itemsets, with probability larger than a specified value. We show that the upper bound is asymptotically tight when w is constant. Our main algorithmic contribution is a progressive sampling approach, combined with suitable stopping conditions, which on appropriate inputs is able to extract approximate top-K frequent itemsets from samples whose sizes are smaller than the general upper bound. In order to test the stopping conditions, this approach maintains the frequency of all itemsets encountered, which is practical only for small w. However, we show how this problem can be mitigated by using a variation of Bloom filters. A number of experiments conducted on both synthetic and real benchmark datasets show that using samples substantially smaller than the original dataset (i.e., of size defined by the upper bound or reached through the progressive sampling approach) enable to approximate the actual top-K frequent itemsets with accuracy much higher than what analytically proved.

Fast approximation of betweenness centrality through sampling

Betweenness centrality is a fundamental measure in social network analysis, expressing the importance or influence of individual vertices (or edges) in a network in terms of the fraction of shortest paths that pass through them. Since exact computation in large networks is prohibitively expensive, we present two efficient randomized algorithms for betweenness estimation. The algorithms are based on random sampling of shortest paths and offer probabilistic guarantees on the quality of the approximation. The first algorithm estimates the betweenness of all vertices (or edges): all approximate values are within an additive factor

Graph summarization with quality guarantees

\varepsilon \in (0,1)

Mining Frequent Itemsets through Progressive Sampling with Rademacher Averages

ε∈(0,1) from the real values, with probability at least