Annotations in Data Streams

Chakrabarti, Amit; Cormode, Graham; McGregor, Andrew; Thaler, Justin

doi:10.1145/2636924

Cited by 26 publications

(131 citation statements)

References 49 publications

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“…In a recent sequence of works, the data stream model was extended to support several interactive and non-interactive proof systems [3,8,12]. The model of streaming algorithms with non-interactive proofs was first introduced in [3] and extended in [8,9].…”

Section: Related Workmentioning

confidence: 99%

“…The model of streaming algorithms with non-interactive proofs was first introduced in [3] and extended in [8,9]. In [3] the authors gave an optimal (up to polylogarithmic factors) data stream with annotations algorithm for computing the k'th frequency moment exactly, for every integer k ≥ 1.…”

Section: Related Workmentioning

confidence: 99%

“…The data stream computational model is an abstraction commonly used for algorithms that process network traffic using sublinear space [1][2][3]. In the settings of this model, we have an algorithm that gets a sequence of elements (typically, each element is an integer) as input.…”

Section: Introductionmentioning

confidence: 99%

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Arthur–Merlin streaming complexity

Gur

Raz

2015

Information and Computation

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We study the power of Arthur-Merlin probabilistic proof systems in the data stream model. We show a canonical AM streaming algorithm for a class of data stream problems. The algorithm offers a tradeoff between the length of the proof and the space complexity that is needed to verify it.As an application, we give an AM streaming algorithm for the Distinct Elements problem. Given a data stream of length m over alphabet of size n, the algorithm uses Õ (s) space and a proof of size Õ (w), for every s, w such that s · w ≥ n (where Õ hides a polylog(m, n) factor). We also prove a lower bound, showing that every MA streaming algorithm for the Distinct Elements problem that uses s bits of space and a proof of size w, satisfies s · w = Ω(n). Furthermore, the lower bound also holds for approximating the number of distinct elements within a multiplicative factor of 1 ± 1/ √ n. As a part of the proof of the lower bound for the Distinct Elements problem, we show a new lower bound of Ω( √ n) on the MA communication complexity of the Gap HammingDistance problem, and prove its tightness.

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Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

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Arthur–Merlin streaming complexity

Gur

Raz

2015

Information and Computation

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“…In a recent line of research, the data stream model was extended to support several interactive and non-interactive proof systems. The model of streaming algorithms with non-interactive proofs was first introduced in (Chakrabarti et al 2014b) and extended in (Chakrabarti et al 2014a(Chakrabarti et al , 2015Cormode et al 2012Cormode et al , 2013Daruki et al 2015;Gur & Raz 2013;Thaler 2014). We remark that there are several related notions between MAPs and annotated data streams.…”

Section: Parameterized Concatenation Problems Our Techniques Formentioning

confidence: 99%

“…MAPs can be thought of as analogous to prescient annotated data streams (see (Chakrabarti et al 2014b) for definitions).…”

mentioning

confidence: 99%

Non-interactive proofs of proximity

Gur

Rothblum

2016

comput. complex.

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We initiate a study of non-interactive proofs of proximity. These proof systems consist of a verifier that wishes to ascertain the validity of a given statement, using a short (sublinear length) explicitly given proof, and a sublinear number of queries to its input. Since the verifier cannot even read the entire input, we only require it to reject inputs that are far from being valid. Thus, the verifier is only assured of the proximity of the statement to a correct one. Such proof systems can be viewed as the N P (or more accurately MA) analogue of property testing. We explore both the power and limitations of non-interactive proofs of proximity. We show that such proof systems can be exponentially stronger than property testers, but are exponentially weaker than the interactive proofs of proximity studied by Rothblum, Vadhan and Wigderson (STOC 2013). In addition, we show a natural problem that has a full and (almost) tight multiplicative trade-off between the length of the proof and the verifier's query complexity. On the negative side, we also show that there exist properties for which even a linearly long (noninteractive) proof of proximity cannot significantly reduce the query complexity.

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Data Stream Verification

Thaler¹

2016

Encyclopedia of Algorithms

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We survey models and algorithms for stream verification. Problem DefinitionStream verification is concerned with the following setting. A computationally limited client wants to compute some property of a massive input, but lacks the resources to store even a small fraction of the input, and hence cannot perform the desired computation locally. The client therefore accesses a powerful but untrusted service provider (e.g., a commercial cloud computing service), who not only performs the requested computation, but also proves that the answer is correct. An array of closely related models have been introduced to capture this scenario. The following section provides a unified presentation of these models, emphasizing their common features before delineating their differences.Stream Verification Model. Let σ = a 1 , a 2 , . . . , a m be a data stream, where each a i comes from a data universe U of size n, and let F be a function mapping data streams to a finite range R. A stream verification protocol for F involves two parties: a prover P, and a (randomized) verifier V. The protocol consists of two stages: a stream observation stage and a proof verification stage.In the stream observation stage, V processes the stream σ, subject to the standard constraints of the data-stream model, i.e., sequential access to σ and limited memory. In the proof verification stage, V and P exchange a sequence of one or more messages, and afterward V outputs a value b. V is allowed to output a special symbol ⊥ indicating a rejection of P's claims. Formally, V constitutes a stream verification protocol if the following two properties are satisfied.• Completeness: There is some prover strategy P such that, for all streams σ, the probability that V outputs F (σ) after interacting with P is at least 2/3.• Soundness: For all streams σ and all prover strategies P, the probability that V outputs a value not in {F (x), ⊥} after interacting with P is at most ǫ ≤ 1/3.Here, the probabilities are taken over V's internal randomness. The constants 2/3 and 1/3 are not essential and are chosen by convention. The parameter ǫ is referred to as the soundness error of the protocol.Costs. There are five primary costs in any stream verification protocol: (1) V's space usage, (2) the total communication cost, (3) V's runtime, (4) P's runtime, and (5) the number of messages exchanged. * Yahoo Labs

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Annotations in Data Streams

Cited by 26 publications

References 49 publications

Arthur–Merlin streaming complexity

Arthur–Merlin streaming complexity

Non-interactive proofs of proximity

Data Stream Verification

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