Separating Adaptive Streaming from Oblivious Streaming Using the Bounded Storage Model

Kaplan, Haim; Mansour, Yishay; Nissim, Kobbi; Stemmer, Uri

doi:10.1007/978-3-030-84252-9_4

Cited by 15 publications

(11 citation statements)

References 20 publications

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“…This shows that "maintaining an O(∆)-coloring of a graph" is a natural (and well-studied) algorithmic problem where, even for insertion-only streams, the space complexities of the robust and standard streaming versions of the problem are well separated: in fact, the separation is roughly quadratic, by taking ∆ = Θ(n). This answers an open question of [KMNS21], as we explain in greater detail in Section 1.2.…”

Section: Our Results and Contributionsmentioning

confidence: 65%

“…This does not quite provide a separation between standard and robust space complexities, since it does not preclude efficient non-linear solutions. The very recent work [KMNS21] gives such a separation: it exhibits a function estimation problem for which the ratio between the adversarial and standard streaming complexities is as large as Ω λ ε,m , which is exponential upon setting parameters appropriately. However, their function is highly artificial, raising the important question: Can a significant gap be shown for a natural streaming problem?…”

Section: Motivation Context and Related Workmentioning

confidence: 99%

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Adversarially Robust Coloring for Graph Streams

Chakrabarti¹,

Ghosh²,

Stoeckl³

2021

Preprint

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A streaming algorithm is considered to be adversarially robust if it provides correct outputs with high probability even when the stream updates are chosen by an adversary who may observe and react to the past outputs of the algorithm. We grow the burgeoning body of work on such algorithms in a new direction by studying robust algorithms for the problem of maintaining a valid vertex coloring of an n-vertex graph given as a stream of edges. Following standard practice, we focus on graphs with maximum degree at most ∆ and aim for colorings using a small number f (∆) of colors.A recent breakthrough (Assadi, Chen, and Khanna; SODA 2019) shows that in the standard, nonrobust, streaming setting, (∆ + 1)-colorings can be obtained while using only O(n) space. Here, we prove that an adversarially robust algorithm running under a similar space bound must spend almost Ω(∆ 2 ) colors and that robust O(∆)-coloring requires a linear amount of space, namely Ω(n∆). We in fact obtain a more general lower bound, trading off the space usage against the number of colors used. From a complexity-theoretic standpoint, these lower bounds provide (i) the first significant separation between adversarially robust algorithms and ordinary randomized algorithms for a natural problem on insertion-only streams and (ii) the first significant separation between randomized and deterministic coloring algorithms for graph streams, since deterministic streaming algorithms are automatically robust.We complement our lower bounds with a suite of positive results, giving adversarially robust coloring algorithms using sublinear space. In particular, we can maintain an O(∆ 2 )-coloring using O(n √ ∆) space and an O(∆ 3 )-coloring using O(n) space.

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Section: Our Results and Contributionsmentioning

confidence: 65%

Section: Motivation Context and Related Workmentioning

confidence: 99%

Adversarially Robust Coloring for Graph Streams

Chakrabarti¹,

Ghosh²,

Stoeckl³

2021

Preprint

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“…We remark that a similar connection to adaptive data analysis was utilized by [KMNS21], in order to show impossibility results for adaptive streaming algorithms. However, our analysis differs significantly as our focus is on runtime lower bounds, while the focus of [KMNS21] was on space lower bounds.…”

Section: Negative Results For An Estimation Problemmentioning

confidence: 99%

Dynamic Algorithms Against an Adaptive Adversary: Generic Constructions and Lower Bounds

Beimel¹,

Kaplan²,

Mansour³

et al. 2021

Preprint

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A dynamic algorithm against an adaptive adversary is required to be correct when the adversary chooses the next update after seeing the previous outputs of the algorithm. We obtain faster dynamic algorithms against an adaptive adversary and separation results between what is achievable in the oblivious vs. adaptive settings. To get these results we exploit techniques from differential privacy, cryptography, and adaptive data analysis.We give a general reduction transforming a dynamic algorithm against an oblivious adversary to a dynamic algorithm robust against an adaptive adversary. This reduction maintains several copies of the oblivious algorithm and uses differential privacy to protect their random bits. Using this reduction we obtain dynamic algorithms against an adaptive adversary with improved update and query times for global minimum cut, all pairs distances, and all pairs effective resistance.We further improve our update and query times by showing how to maintain a sparsifier over an expander decomposition that can be refreshed fast. This fast refresh enables it to be robust against what we call a blinking adversary that can observe the output of the algorithm only following refreshes. We believe that these techniques will prove useful for additional problems.On the flip side, we specify dynamic problems that, assuming a random oracle, every dynamic algorithm that solves them against an adaptive adversary must be polynomially slower than a rather straightforward dynamic algorithm that solves them against an oblivious adversary. We first show a separation result for a search problem and then show a separation result for an estimation problem. In the latter case our separation result draws from lower bounds in adaptive data analysis.

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“…The connection between differential privacy and adaptive generalization also originated from Dwork et al (2015b). Interestingly, this connection has recently been repurposed for different settings, such as adversarial streaming and dynamic algorithms (Hassidim et al, 2020;Attias et al, 2021;Kaplan et al, 2021;Beimel et al, 2021).…”

Section: Other Related Workmentioning

confidence: 98%

Adaptive Data Analysis with Correlated Observations

Kontorovich¹,

Sadigurschi²,

Stemmer³

2022

Preprint

Self Cite

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The vast majority of the work on adaptive data analysis focuses on the case where the samples in the dataset are independent. Several approaches and tools have been successfully applied in this context, such as differential privacy, max-information, compression arguments, and more. The situation is far less well-understood without the independence assumption.We embark on a systematic study of the possibilities of adaptive data analysis with correlated observations. First, we show that, in some cases, differential privacy guarantees generalization even when there are dependencies within the sample, which we quantify using a notion we call Gibbs-dependence. We complement this result with a tight negative example. Second, we show that the connection between transcript-compression and adaptive data analysis can be extended to the non-iid setting.

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Separating Adaptive Streaming from Oblivious Streaming Using the Bounded Storage Model

Cited by 15 publications

References 20 publications

Adversarially Robust Coloring for Graph Streams

Adversarially Robust Coloring for Graph Streams

Dynamic Algorithms Against an Adaptive Adversary: Generic Constructions and Lower Bounds

Adaptive Data Analysis with Correlated Observations

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