Search for: All records

d-dimensional (for d > 1) efficient range-summability (dD-ERS) of random variables (RVs) is a fundamental algorithmic problem that has applications to two important families of database problems, namely, fast approximate wavelet tracking (FAWT) on data streams and approximately answering range-sum queries over a data cube. Whether there are efficient solutions to the dD-ERS problem, or to the latter database problem, have been two long-standing open problems. Both are solved in this work. Specifically, we propose a novel solution framework to dD-ERS on RVs that have Gaussian or Poisson distribution. Our dD-ERS solutions are the first ones that have polylogarithmic time complexities. Furthermore, we develop a novel k-wise independence theory that allows our dD-ERS solutions to have both high computational efficiencies and strong provable independence guarantees. Finally, we show that under a sufficient and likely necessary condition, certain existing solutions for 1D-ERS can be generalized to higher dimensions. 

In this work, we formulate and solve a new type of approximate nearest neighbor search (ANNS) problems called ANNS after linear transformation (ALT). In ANNS-ALT, we search for the vector (in a dataset) that, after being linearly transformed by a user-specified query matrix, is closest to a query vector. It is a very general mother problem in the sense that a wide range of baby ANNS problems that have important applications in databases and machine learning can be reduced to and solved as ANNS-ALT, or its dual that we call ANNS-ALTD. We propose a novel and computationally efficient solution, called ONe Index for All Kernels (ONIAK), to ANNS-ALT and all its baby problems when the data dimension 𝑑 is not too large (say 𝑑 ≤ 200). In ONIAK, a universal index is built, once and for all, for answering all future ANNS-ALT queries that can have distinct query matrices. We show by experiments that, when 𝑑 is not too large, ONIAK has better query performance than linear scan on the mother problem (of ANNS-ALT), and has query performances comparable to those of the state-of-the-art solutions on the baby problems. However, the algorithmic technique behind this universal index approach suffers from a so-called dimension blowup problem that can make the indexing time prohibitively long for a large dataset. We propose a novel algorithmic technique, called fast GOE quadratic form (FGoeQF), that completely solves the (prohibitively long indexing time) fallout of the dimension blowup problem. We also propose a Johnson-Lindenstrauss transform (JLT) based ANNS- ALT (and ANNS-ALTD) solution that significantly outperforms any competitor when 𝑑 is large. 

Efficient range-summability (ERS) of a long list of random variables is a fundamental algorithmic problem that has applications to three important database applications, namely, data stream processing, space-efficient histogram maintenance (SEHM), and approximate nearest neighbor searches (ANNS). In this work, we propose a novel dyadic simulation framework and develop three novel ERS solutions, namely Gaussian-dyadic simulation tree (DST), Cauchy-DST and Random Walk-DST, using it. We also propose novel rejection sampling techniques to make these solutions computationally efficient. Furthermore, we develop a novel k-wise independence theory that allows our ERS solutions to have both high computational efficiencies and strong provable independence guarantees. 

With the booming of online service systems, anomaly detection on multivariate time series, such as a combination of CPU utilization, average response time, and requests per second, is important for system reliability. Although a collection of learning-based approaches have been designed for this purpose, our empirical study shows that these approaches suffer from long initialization time for sufficient training data. In this paper, we introduce the Compressed Sensing technique to multivariate time series anomaly detection for rapid initialization. To build a jump-starting anomaly detector, we propose an approach named JumpStarter. Based on domainspecific insights, we design a shape-based clustering algorithm as well as an outlier-resistant sampling algorithm for JumpStarter.With real-world multivariate time series datasets collected from two Internet companies, our results show that JumpStarter achieves an average F1 score of 94.12%, significantly outperforming the state-of-the-art anomaly detection algorithms, with a much shorter initialization time of twenty minutes. We have applied JumpStarter in online service systems and gained useful lessons in real-world scenarios. 

Set reconciliation is a fundamental algorithmic problem that arises in many networking, system, and database applications. In this problem, two large sets A and B of objects (bitcoins, files, records, etc.) are stored respectively at two different network-connected hosts, which we name Alice and Bob respectively. Alice and Bob communicate with each other to learn A Δ B , the difference between A and B , and as a result the reconciled set A ∪ B. Current set reconciliation schemes are based on either invertible Bloom filters (IBF) or error-correction codes (ECC). The former has a low computational complexity of O(d) , where d is the cardinality of A Δ B , but has a high communication overhead that is several times larger than the theoretical minimum. The latter has a low communication overhead close to the theoretical minimum, but has a much higher computational complexity of O(d 2 ). In this work, we propose Parity Bitmap Sketch (PBS), an ECC-based set reconciliation scheme that gets the better of both worlds: PBS has both a low computational complexity of O(d) just like IBF-based solutions and a low communication overhead of roughly twice the theoretical minimum. A separate contribution of this work is a novel rigorous analytical framework that can be used for the precise calculation of various performance metrics and for the near-optimal parameter tuning of PBS.