Heavy Hitters via Cluster-Preserving Clustering

Larsen, Kasper Green; Nelson, Jelani; Nguyêݱn, Huy L.; Thorup, Mikkel

doi:10.1109/focs.2016.16

Cited by 44 publications

(39 citation statements)

References 41 publications

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“…However, there are currently no explicit codes achieving the parameter settings that are needed for the construction. To overcome this issue, Larsen et al [22] constructed a relaxed variant of list-recoverable codes, and showed that their relaxed variant still suffices for their (non-private) reduction. Intuitively, their relaxed code utilizes the randomness in the first portion of every element in the lists (i.e., the outcome of the hash functions).…”

Section: A Non-private Reductionmentioning

confidence: 99%

“…Formally, For completeness, we include the proof in Appendix B. In the following sections we construct a private version of the algorithm of [22] and show that it achieves optimal error in all parameters. We remark that the focus in [22] was on space and runtime, and that in fact, in the non-private literature the meaning of "minimal achievable error" is unclear, as achieving zero error is trivial (it is "only" a question of runtime and memory).…”

Section: A Non-private Reductionmentioning

confidence: 99%

“…In this work we combine ideas from the recent locally-private heavy-hitters algorithm of [3] with the recent non-private algorithm of [22], and present a new efficient LDP heavy-hitters algorithm achieving optimal worst-case error ∆ as a function of the number of users n, the size of the domain |X|, the privacy parameter ε, and the failure probability β. Prior state-of-the-art results [4,3] either obtained error with sub-optimal dependence on the failure probability β, or had runtime at least linear in |X| (which is not realistic in real applications, where X may be the space of all reasonable-length URL domains).…”

Section: Introductionmentioning

confidence: 99%

“…[22]). There exist constants C > 1 and 0 < α < 1 such that the following holds.For all constants M ≤ log |X| and Y, ∈ N, and for every fixed choice of functions h 1 , .…”

mentioning

confidence: 99%

“…We remark that this presentation is oversimplified. In the analysis of[22], the problem is not only that each x * causes a small fraction of the hash functions to fail. Rather, the problem is that a small fraction of the coordinates are "bad" (since otherwise it may be that each x is failed by very few hash functions, but every hm ends up "bad" because they fail for some different x's).…”

mentioning

confidence: 99%

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Heavy Hitters and the Structure of Local Privacy

Bun

Nelson

Stemmer

2018

Proceedings of the 37th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems

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105

141

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We present a new locally differentially private algorithm for the heavy hitters problem which achieves optimal worst-case error as a function of all standardly considered parameters. Prior work obtained error rates which depend optimally on the number of users, the size of the domain, and the privacy parameter, but depend sub-optimally on the failure probability.We strengthen existing lower bounds on the error to incorporate the failure probability, and show that our new upper bound is tight with respect to this parameter as well. Our lower bound is based on a new understanding of the structure of locally private protocols. We further develop these ideas to obtain the following general results beyond heavy hitters.• Advanced Grouposition: In the local model, group privacy for k users degrades proportionally to ≈ √ k, instead of linearly in k as in the central model. Stronger group privacy yields improved max-information guarantees, as well as stronger lower bounds (via "packing arguments"), over the central model.• Building on a transformation of Bassily and Smith (STOC 2015), we give a generic transformation from any non-interactive approximate-private local protocol into a pure-private local protocol. Again in contrast with the central model, this shows that we cannot obtain more accurate algorithms by moving from pure to approximate local privacy.

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Section: A Non-private Reductionmentioning

confidence: 99%

Section: A Non-private Reductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…[22]). There exist constants C > 1 and 0 < α < 1 such that the following holds.For all constants M ≤ log |X| and Y, ∈ N, and for every fixed choice of functions h 1 , .…”

mentioning

confidence: 99%

mentioning

confidence: 99%

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Heavy Hitters and the Structure of Local Privacy

Bun

Nelson

Stemmer

2018

Proceedings of the 37th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems

Self Cite

105

141

View full text Add to dashboard Cite

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Utilizing the column imprints to accelerate no‐partitioning hash joins in large‐scale edge systems

Liu

2020

Trans Emerging Tel Tech

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With the increasing number of edge devices in large-scale edge systems, more and more data are collected to be processed. In such big data scenarios, there is a resurgence of interest in main-memory analytic databases because of the large RAM capacity of modern servers and the increasing demand for real-time analytic platforms. In such databases, join is at the heart of almost every query plan. Join also stays as a time-consuming operation when the denormalization overhead is too large to be applicable. However, the current implementations of these operations have not fully leveraged the new features (eg, SIMD, multi-core) provided by the modern hardware. The goal of this article is to design efficient algorithms for joins by judiciously exploiting every bit of RAM and all the available parallelisms in each processing unit. For join operations, hash joins have been studied, improved, and reexamined over decades.In this article, we propose to utilize a secondary index to improve hash joins without the physical partitioning. Specifically, in the build phase, the hash values are scattered evenly into the logical partitions of the hash table; in the probe phase, the secondary index is used as the hints to re-order the probing sequence, such that the locality of the hash probing is increased. We benchmark the performance of the proposed techniques in our column-store research prototype. Extensive experiments on the synthetic data and the real data show that our methods offer significant performance improvement over their counterparts.

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