Given a social network G , a cost associated with each user, and an influence threshold η, the minimum cost seed selection problem (MCSS) aims to find a set of seeds that minimizes the total cost to reach η users. Existing works are mainly devoted to providing an expected coverage guarantee on reaching η, classified as MCSS-ECG, where their solutions either rely on an impractical influence oracle or cannot attain the expected influence threshold. More importantly, due to the expected coverage guarantee, the actual influence in a campaign may drift from the threshold evidently. Thus, the advertisers would like to request for a probability guarantee of reaching η. This motivates us to further solve the MCSS problem with a probabilistic coverage guarantee, termed MCSS-PCG. In this paper, we first propose our algorithm CLEAR to solve MCSS-ECG, which reaches the expected influence threshold without any influence oracle or influence shortfall but a practical approximation ratio. However, the ratio involves an unknown term (i.e., the optimal cost). Thus, we further devise the STAR method to derive a lower bound of the optimal cost and then obtain the first explicit approximation ratio for MCSS-ECG. In MCSS-PCG, it is necessary to estimate the probability that the current seeds reach η, to decide when to stop seed selection. To achieve this, we design a new technique named MRR, which provides efficient probability estimation with a theoretical guarantee. With MRR in hand, we propose our algorithm SCORE for MCSS-PCG, whose performance guarantee is derived by measuring the gap between MCSS-ECG and MCSS-PCG, and applying the theoretical results in MCSS-ECG. Finally, extensive experiments demonstrate that our algorithms achieve up to two orders of magnitude speed-up compared to alternatives while meeting the requirement of MCSS-PCG with the smallest cost.

Trend analysis is a fundamental type of analytical query in online analytical processing (OLAP) systems. In trend analysis, a key step is to identify k valuable attributes whose distributions in two subsets under different predicates significantly differ for further investigation, where the difference is measured by metric functions. However, the exact solution that involves scanning all records is prohibitively expensive, particularly when handling large datasets in the era of big data. To minimize unnecessary data access, the existing state-of-the-art solution TopKAttr adopts sampling to avoid the expensive data scan. However, their solution still has two main drawbacks. Firstly, their solution is tailored only for two limited metric functions: the Earth Mover distance and Euclidean distance, and cannot be generalized to more complicated metric functions. Besides, their solution still aims to return the exact top-k answers via the sampling method, which still causes high running costs as shown in our experiment. Motivated by these limitations, we propose a general approximation framework for attribute recommendation that efficiently returns the top-k attributes with theoretical guarantees while supporting an extensive range of metric functions, such as the Kolmogorov-Smirnov test (KS-test), Chebyshev distance, the Earth Mover distance, Euclidean distance, and with the potential to more metrics. The key to our framework is a new bound estimation strategy that can be applied to a wide spectrum of metrics, as we listed above. Based on our estimation framework, we further devise an efficient approximation algorithm with theoretical guarantees to answer the top-k queries, which is widely used in attribute recommendation. Extensive experiments on four real large datasets show that our framework gains up to an order of magnitude speed-up and consistently high accuracy compared to TopKAttr, providing a promising alternative for attribute recommendation in OLAP systems.

A recent line of works apply machine learning techniques to assist or rebuild cost-based query optimizers in DBMS. While exhibiting superiority in some benchmarks, their deficiencies, e.g., unstable performance, high training cost, and slow model updating, stem from the inherent hardness of predicting the cost or latency of execution plans using machine learning models. In this paper, we introduce a learning-to-rank query optimizer, called Lero, which builds on top of a native query optimizer and continuously learns to improve the optimization performance. The key observation is that the relative order or rank of plans, rather than the exact cost or latency, is sufficient for query optimization. Lero employs a pairwise approach to train a classifier to compare any two plans and tell which one is better. Such a binary classification task is much easier than the regression task to predict the cost or latency, in terms of model efficiency and accuracy. Rather than building a learned optimizer from scratch, Lero is designed to leverage decades of wisdom of databases and improve the native query optimizer. With its non-intrusive design, Lero can be implemented on top of any existing DBMS with minimal integration efforts. We implement Lero and demonstrate its outstanding performance using PostgreSQL. In our experiments, Lero achieves near optimal performance on several benchmarks. It reduces the plan execution time of the native optimizer in PostgreSQL by up to 70% and other learned query optimizers by up to 37%. Meanwhile, Lero continuously learns and automatically adapts to query workloads and changes in data.

Empirical variance is a fundamental concept widely used in data management and data analytics, e.g., query optimization, approximate query processing, and feature selection. A direct solution to derive the empirical variance is scanning the whole data table, which is expensive when the data size is huge. Hence, most current works focus on approximate answers by sampling. For results with approximation guarantees, the samples usually need to be uniformly independent random, incurring high cache miss rates especially in compact columnar style layouts. An alternative uses block sampling to avoid this issue, which directly samples a block of consecutive records fitting page sizes instead of sampling one record each time. However, this provides no theoretical guarantee. Existing studies show that the practical estimations can be inaccurate as the records within a block can be correlated.

Empirical entropy is a classic concept in data mining and the foundation of many other important concepts like mutual information. However, computing the exact empirical entropy/mutual information on large datasets can be expensive. Some recent research work explores sampling techniques on the empirical entropy/mutual information to speed up the top-k and filtering queries. However, their solution still aims to return the exact answers to the queries, resulting in high computational costs.

Personalized PageRank (PPR) has wide applications in search engines, social recommendations, community detection, and so on. Nowadays, graphs are becoming massive and many IT companies need to deal with large graphs that cannot be fitted into the memory of most commodity servers. However, most existing state-of-the-art solutions for PPR computation only work for single-machines and are inefficient for the distributed framework since such solutions either (i) result in an excessively large number of communication rounds, or (ii) incur high communication costs in each round. Motivated by this, we present Delta-Push , an efficient framework for single-source and top- k PPR queries in distributed settings. Our goal is to reduce the number of rounds while guaranteeing that the load, i.e., the maximum number of messages an executor sends or receives in a round, can be bounded by the capacity of each executor. We first present a non-trivial combination of a redesigned parallel push algorithm and the Monte-Carlo method to answer single-source PPR queries. The solution uses pre-sampled random walks to reduce the number of rounds for the push al6gorithm. Theoretical analysis under the Massively Parallel Computing (MPC) model shows that our proposed solution bounds the communication rounds to [EQUATION] under a load of O ( m/p ), where m is the number of edges of the input graph, p is the number of executors, and ϵ is a user-defined error parameter. In the meantime, as the number of executors increases to p' = γ · p , the load constraint can be relaxed since each executor can hold O (γ · m/p' ) messages with invariant local memory. In such scenarios, multiple queries can be processed in batches simultaneously. We show that with a load of O (γ · m/p' ), our Delta-Push can process γ queries in a batch with [EQUATION] rounds, while other baseline solutions still keep the same round cost for each batch. We further present a new top- k algorithm that is friendly to the distributed framework and reduces the number of rounds required in practice. Extensive experiments show that our proposed solution is more efficient than alternatives.