Fast concurrent data sketches

Rinberg, Arik; Spiegelman, Alexander; Bortnikov, Edward; Hillel, Eshcar; Keidar, Idit; Rhodes, Lee; Serviansky, Hadar

doi:10.1145/3332466.3374512

Cited by 6 publications

(17 citation statements)

References 15 publications

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“…Alistarh et al expand upon this and define distributional linearizability [2], which requires a distribution over the internal states of the object for its error analysis. Rinberg et al consider strongly linearizable r-relaxed semantics for randomized objects [30]. We differ from these works in two points: First, a sequential history of an IVL object must adhere to the sequential specification, whereas in these relaxations even a sequential history may diverge from the specification.…”

Section: Relationship To Other Relaxationsmentioning

confidence: 97%

“…The ever increasing rates of incoming data create a strong demand for parallel stream processing [8,18]. In order to allow queries to return fresh results in real-time without hampering data ingestion, it is paramount to support queries concurrently with updates [30,31]. But parallelizing sketches raises some important questions, for instance: What are the semantics of overlapping operations in a concurrent sketch?, How can we prove error guarantees for such a sketch?, and, in particular, Can we reuse the myriad of clever analyses of existing sketches' error bounds in parallel settings without opening the black box?…”

Section: Motivationmentioning

confidence: 99%

“…Proving an error bound for an efficient parallel implementation of the CM sketch for existing criteria is not trivial. Using the framework defined by Rinberg et al [30] requires the query to take a strongly linearizable snapshot of the matrix [28]. Distributional linearizability [2] necessitates an analysis of the error bounds directly in the concurrent setting, without leveraging the sketch's existing analysis for the sequential setting.…”

Section: Concurrent Countmin Sketchmentioning

confidence: 99%

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Intermediate Value Linearizability: A Quantitative Correctness Criterion

Rinberg¹,

Keidar²

2020

Preprint

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Big data processing systems often employ batched updates and data sketches to estimate certain properties of large data. For example, a CountMin sketch approximates the frequencies at which elements occur in a data stream, and a batched counter counts events in batches. This paper focuses on correctness criteria for concurrent implementations of such objects. Specifically, we consider quantitative objects, whose return values are from a totally ordered domain, with a particular emphasis on ( , δ)-bounded objects that estimate a numerical quantity with an error of at most with probability at least 1 − δ.The de facto correctness criterion for concurrent objects is linearizability. Intuitively, under linearizability, when a read overlaps an update, it must return the object's value either before the update or after it. Consider, for example, a single batched increment operation that counts three new events, bumping a batched counter's value from 7 to 10. In a linearizable implementation of the counter, a read overlapping this update must return either 7 or 10. We observe, however, that in typical use cases, any intermediate value between 7 and 10 would also be acceptable. To capture this additional degree of freedom, we propose Intermediate Value Linearizability (IVL), a new correctness criterion that relaxes linearizability to allow returning intermediate values, for instance 8 in the example above. Roughly speaking, IVL allows reads to return any value that is bounded between two return values that are legal under linearizability.A key feature of IVL is that we can prove that concurrent IVL implementations of ( , δ)-bounded objects are themselves ( , δ)-bounded. To illustrate the power of this result, we give a straightforward and efficient concurrent implementation of an ( , δ)-bounded CountMin sketch, which is IVL (albeit not linearizable).Finally, we show that IVL allows for inherently cheaper implementations than linearizable ones. In particular, we show a lower bound of Ω(n) on the step complexity of the update operation of any wait-free linearizable batched counter, and propose a wait-free IVL implementation of the same object with an O(1) step complexity for update.

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Section: Relationship To Other Relaxationsmentioning

confidence: 97%

Section: Motivationmentioning

confidence: 99%

Section: Concurrent Countmin Sketchmentioning

confidence: 99%

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Intermediate Value Linearizability: A Quantitative Correctness Criterion

Rinberg¹,

Keidar²

2020

Preprint

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“…Finally, Section 8 concludes. The full paper [24] formally proves strong linearisability of our generic algorithm, and includes some of the mathematical derivations used in our analysis.…”

Section: Main Contributionmentioning

confidence: 98%

“…Accuracy is defined in one of two ways. One approach analyses the Relative Standard Error (RSE) of the estimate, formally defined in the full paper [24],which is the standard error normalized by the quantity being estimated. For example, a KMV Θ sketch with k samples has an RSE of less than 1/ √ k − 2 [12].…”

Section: Modelmentioning

confidence: 99%

Fast Concurrent Data Sketches

Rinberg

Spiegelman

Bortnikov³

et al. 2019

Proceedings of the 2019 ACM Symposium on Principles of Distributed Computing

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Data sketches are approximate succinct summaries of long data streams. They are widely used for processing massive amounts of data and answering statistical queries about it. Existing libraries producing sketches are very fast, but do not allow parallelism for creating sketches using multiple threads or querying them while they are being built. We present a generic approach to parallelising data sketches efficiently and allowing them to be queried in real time, while bounding the error that such parallelism introduces. Utilising relaxed semantics and the notion of strong linearisability we prove our algorithm's correctness and analyse the error it induces in two specific sketches. Our implementation achieves high scalability while keeping the error small. We have contributed one of our concurrent sketches to the open-source data sketches library.

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