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 ε ∈ (0, 1) from the real values, with probability at least 1 − δ. The second algorithm focuses on the top-K vertices (or edges) with highest betweenness and estimate their betweenness value to within a multiplicative factor ε, with probability at least 1 − δ. This is the first algorithm that can compute such approximation for the top-K vertices (or edges). By proving upper and lower bounds to the VC-dimension of a range set associated with the problem at hand, we can bound the sample size needed to achieve the desired approximations. We obtain sample sizes that are independent from the number of vertices in the network and only depend on a characteristic quantity that we call the vertex-diameter, that is the maximum number of vertices in a shortest path. In some cases, the sample size is completely independent from any quantitative property of the graph. An extensive experimental evaluation on real and artificial networks shows that our algorithms are significantly faster and much more scalable as the number of vertices grows than other algorithms with similar approximation guarantees.

Abstract-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 learningbased 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 operatorlevel 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 PostgreSQL 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.

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We study the problem of graph summarization. Given a large graph we aim at producing a concise lossy representation that can be stored in main memory and used to approximately answer queries about the original graph much faster than by using the exact representation. In this paper we study a very natural type of summary: the original set of vertices is partitioned into a small number of supernodes connected by superedges to form a complete weighted graph. The superedge weights are the edge densities between vertices in the corresponding supernodes. The goal is to produce a summary that minimizes the reconstruction error w.r.t. the original graph. By exposing a connection between graph summarization and geometric clustering problems (i.e., k-means and k-median), we develop the first polynomial-time approximation algorithm to compute the best possible summary of a given size.

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

We present an algorithm to extract an high-quality approximation of the (top-k) Frequent itemsets (FIs) from random samples of a transactional dataset. With high probability the approximation is a superset of the FIs, and no itemset with frequency much lower than the threshold is included in it. The algorithm employs progressive sampling, with a stopping condition based on bounds to the empirical Rademacher average, a key concept from statistical learning theory. The computation of the bounds uses characteristic quantities that can be obtained efficiently with a single scan of the sample. Therefore, evaluating the stopping condition is fast, and does not require an expensive mining of each sample. Our experimental evaluation confirms the practicality of our approach on real datasets, outperforming approaches based on one-shot static sampling.

The tasks of extracting (top-K) Frequent Itemsets (FIs) and Association Rules (ARs) are fundamental primitives in data mining and database applications. Exact algorithms for these problems exist and are widely used, but their running time is hindered by the need of scanning the entire dataset, possibly multiple times. High-quality approximations of FIs and ARs are sufficient for most practical uses. Sampling techniques can be used for fast discovery of approximate solutions, but works exploring this technique did not provide satisfactory performance guarantees on the quality of the approximation due to the difficulty of bounding the probability of under-or oversampling any one of an unknown number of frequent itemsets. We circumvent this issue by applying the statistical concept of Vapnik-Chervonenkis (VC) dimension to develop a novel technique for providing tight bounds on the sample size that guarantees approximation of the (top-K) FIs and ARs within user-specified parameters. The resulting sample size is linearly dependent on the VC-dimension of a range space associated with the dataset. We analyze the VC-dimension of this range space and show that it is upper bounded by an easy-to-compute characteristic quantity of the dataset, the d-index, namely, the maximum integer d such that the dataset contains at least d transactions of length at least d such that no one of them is a superset of or equal to another. We show that this bound is tight for a large class of datasets. The resulting sample size is a significant improvement over previous known results. We present an extensive experimental evaluation of our technique on real and artificial datasets, demonstrating the practicality of our methods, and showing that they achieve even higher quality approximations than what is guaranteed by the analysis. ACM Reference Format:Matteo Riondato and Eli Upfal. 2014. Efficient discovery of association rules and frequent itemsets through sampling with tight performance guarantees.

Abstract. 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.