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Bloom Filters are a desirable data structure for distinguishing new values in sequences of data (i.e., messages), due to their space efficiency, their low false positive rates (incorrectly classifying a new value as a repeat), and never producing false negatives (classifying a repeat value as new). However, as the Bloom Filter's bits are filled, false positive rates creep upward. To keep false positive rates below a reasonable threshold, applications periodically "recycle" the Bloom Filter, clearing the memory and then resuming the tracking of data. After a recycle point, subsequent arrivals of recycled messages are likely to be misclassified as new; recycling induces false negatives. Despite numerous applications of recycling, the corresponding false negative rates have never been analyzed. In this paper, we derive approximations, upper bounds, and lower bounds of false negative rates for several variants of recycling Bloom Filters. These approximations and bounds are functions of the size of memory used to store the Bloom Filter and the distributions on new arrivals and repeat messages, and can be efficiently computed on conventional hardware. We show, via comparison to simulation, that our upper bounds and approximations are extremely tight, and can be efficiently computed for megabyte-sized Bloom Filters on conventional hardware.more » « less
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Bloom Filters are a space-efficient data structure used for the testing of membership in a set that errs only in the False Positive direction. However, the standard analysis that measures this False Positive rate provides a form of worst case bound that is both overly conservative for the majority of network applications that utilize Bloom Filters, and reduces accuracy by not taking into account the actual state (number of bits set) of the Bloom Filter after each arrival. In this paper, we more accurately characterize the False Positive dynamics of Bloom Filters as they are commonly used in networking applications. In particular, network applications often utilize a Bloom Filter that “recycles”: it repeatedly fills, and upon reaching a certain level of saturation, empties and fills again. In this context, it makes more sense to evaluate performance using the average False Positive rate instead of the worst case bound. We show how to efficiently compute the average False Positive rate of recycling Bloom Filter variants via renewal and Markov models. We apply our models to both the standard Bloom Filter and a “two-phase” variant, verify the accuracy of our model with simulations, and find that the previous analysis’ worst-case formulation leads to up to a 30% reduction in the efficiency of Bloom Filter when applied in network applications, while two-phase overhead diminishes as the needed False Positive rate is tightened.more » « lessFree, publicly-accessible full text available May 20, 2025
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Building interactive data interfaces is hard because the design of an interface depends on the data processing needs for the underlying analysis task, yet we do not have a good representation for analysis tasks. To fill this gap, this paper advocates for a Data Interface Grammar (DIG) as an intermediate representation of analysis tasks. We show that DIG is compatible with existing data engineering practices, compact to represent any analysis, simple to translate into an interface design, and amenable to offline analysis. We further illustrate the potential benefits of this abstraction, such as automatic interface generation, automatic interface backend optimization, tutorial generation, and workload generation.more » « less
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We present a novel multi-level representation of time series called OM3 that facilitates efficient interactive progressive visualization of large data stored in a database and supports various interactions such as resizing, panning, zooming, and visual query. Based on our proposed line-segment aggregation, this representation can produce error-free line visualizations that preserve the shape of a time series in windows of arbitrary sizes. To reduce the interaction latency, we develop an incremental tree-based query strategy to support progressive visualizations, allowing a finer control on the accuracy-time tradeoff. We quantitatively compare OM3 with state-of-the-art methods, including a method implemented on a leading time-series database InfluxDB, in two settings with databases residing either in the local area network or on the cloud. Results show that OM^3 maintains a low latency within 300~ms on the web browser and a high data reduction ratio regardless of the data size (ranging from millions to billions of records), achieving around 1,000 times faster than the state-of-the-art methods on the largest dataset experimented with.