License: 
Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.DISC.2020.2
URN: urn:nbn:de:0030-drops-130801
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/13080/
Rinberg, Arik ;
Keidar, Idit
Intermediate Value Linearizability: A Quantitative Correctness Criterion
Abstract
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 (ε,δ)-bounded objects that estimate a numerical quantity with an error of at most ε 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 (ε,δ)-bounded objects are themselves (ε,δ)-bounded. To illustrate the power of this result, we give a straightforward and efficient concurrent implementation of an (ε, 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 from single-writer objects, and propose a wait-free IVL implementation of the same object with an O(1) step complexity for update.
BibTeX - Entry
@InProceedings{rinberg_et_al:LIPIcs:2020:13080,
author = {Arik Rinberg and Idit Keidar},
title = {{Intermediate Value Linearizability: A Quantitative Correctness Criterion}},
booktitle = {34th International Symposium on Distributed Computing (DISC 2020)},
pages = {2:1--2:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-168-9},
ISSN = {1868-8969},
year = {2020},
volume = {179},
editor = {Hagit Attiya},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2020/13080},
URN = {urn:nbn:de:0030-drops-130801},
doi = {10.4230/LIPIcs.DISC.2020.2},
annote = {Keywords: concurrency, concurrent objects, linearizability}
}
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Keywords: |
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concurrency, concurrent objects, linearizability |
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Collection: |
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34th International Symposium on Distributed Computing (DISC 2020) |
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Issue Date: |
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2020 |
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Date of publication: |
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07.10.2020 |
