For decades, the join operator over fast data streams has always drawn much attention from the database community, due to its wide spectrum of real-world applications, such as online clustering, intrusion detection, sensor data monitoring, and so on. Existing works usually assume that the underlying streams to be joined are complete (without any missing values). However, this assumption may not always hold, since objects from streams may contain some missing attributes, due to various reasons such as packet losses, network congestion failure, and so on. In this paper, we formalize an important problem, namely join over incomplete data streams (Join-iDS), which retrieves joining object pairs from incomplete data streams with high confidences. We tackle the Join-iDS problem in the style of "data imputation and query processing at the same time". To enable this style, we design an effective and efficient cost-model-based imputation method via deferential dependency (DD), devise effective pruning strategies to reduce the Join-iDS search space, and propose efficient algorithms via our proposed cost-model-based data synopsis indexes. Extensive experiments have been conducted to verify the efficiency and effectiveness of our proposed Join-iDS approach on both real and synthetic data sets.
We consider the problem of approximating sliding window joins over data streams in a data stream processing system with limited resources. In our model, we deal with resource constraints by shedding load in the form of dropping tuples from the data streams. We first discuss alternate architectural models for data stream join processing, and we survey suitable measures for the quality of an approximation of a set-valued query result. We then consider the number of generated result tuples as the quality measure, and we give optimal offline and fast online algorithms for it. In a thorough experimental study with synthetic and real data we show the efficacy of our solutions. For applications with demand for exact results we introduce a new Archive-metric which captures the amount of work needed to complete the join in case the streams are archived for later processing. The join operation is one of the fundamental relational database query operations. It facilitates the retrieval of information from two different relations based on a Cartesian product of the two relations. The join is one of the most diffidult operations to implement efficiently, as no predefined links between relations are required to exist (as they are with network and hierarchical systems). The join is the only relational algebra operation that allows the combining of related tuples from relations on different attribute schemes. Since it is executed frequently and is expensive, much research effort has been applied to the optimization of join processing. In this paper, the different kinds of joins and the various implementation techniques are surveyed. These different methods are classified based on how they partition tuples from different relations. Some require that all tuples from one be compared to all tuples from another; other algorithms only compare some tuples from each. In addition, some techniques perform an explicit partitioning, whereas others are implicit. Similarity join (SJ) in time-series databases has a wide spectrum of applications such as data cleaning and mining. Specifically, an SJ query retrieves all pairs of (sub)sequences from two time-series databases that epsiv-match with each other, where epsiv is the matching threshold. Previous work on this problem usually considers static time-series databases, where queries are performed either on disk-based multidimensional indexes built on static data or by nested loop join (NLJ) without indexes. SJ over multiple stream time series, which continuously outputs pairs of similar subsequences from stream time series, strongly requires low memory consumption, low processing cost, and query procedures that are themselves adaptive to time-varying stream data. These requirements invalidate the existing approaches in static databases. In this paper, we propose an efficient and effective approach to perform SJ among multiple stream time series incrementally. In particular, we present a novel method, Adaptive Radius-based Search (ARES), which can answer the similarity search without false dismissals and is seamlessly integrated into SJ processing. Most importantly, we provide a formal cost model for ARES, based on which ARES can be adaptive to data characteristics, achieving the minimum number of refined candidate pairs, and thus, suitable for stream processing. Furthermore, in light of the cost model, we utilize space-efficient synopses that are constructed for stream time series to further reduce the candidate set. Extensive experiments demonstrate the efficiency and effectiveness of our proposed approach. Similarity join processing in the streaming environment has many practical applications such as sensor networks, object tracking and monitoring, and so on. Previous works usually assume that stream processing is conducted over precise data. In this paper, we study an important problem of similarity join processing on stream data that inherently contain uncertainty (or called uncertain data streams), where the incoming data at each time stamp are uncertain and imprecise. Specifically, we formalize this problem as join on uncertain data streams (USJ), which can guarantee the accuracy of USJ answers over uncertain data. To tackle the challenges with respect to efficiency and effectiveness such as limited memory and small response time, we propose effective pruning methods on both object and sample levels to filter out false alarms. We integrate the proposed pruning methods into an efficient query procedure that can incrementally maintain the USJ answers. Most importantly, we further design a novel strategy, namely, adaptive superset prejoin (ASP), to maintain a superset of USJ candidate pairs. ASP is in light of our proposed formal cost model such that the average USJ processing cost is minimized. We have conducted extensive experiments to demonstrate the efficiency and effectiveness of our proposed approaches.