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1. Model Counting Meets F 0 Estimation

   https://doi.org/10.1145/3603496  

   Pavan, A. ; Vinodchandran, N. V. ; Bhattacharyya, Arnab ; Meel, Kuldeep S. ( September 2023 , ACM Transactions on Database Systems)

   Constraint satisfaction problems (CSPs) and data stream models are two powerful abstractions to capture a wide variety of problems arising in different domains of computer science. Developments in the two communities have mostly occurred independently and with little interaction between them. In this work, we seek to investigate whether bridging the seeming communication gap between the two communities may pave the way to richer fundamental insights. To this end, we focus on two foundational problems: model counting for CSP’s and computation of zeroth frequency moments (F₀) for data streams.

   Our investigations lead us to observe a striking similarity in the core techniques employed in the algorithmic frameworks that have evolved separately for model counting andF₀computation. We design a recipe for translating algorithms developed forF₀estimation to model counting, resulting in new algorithms for model counting. We also provide a recipe for transforming sampling algorithm over streams to constraint sampling algorithms. We then observe that algorithms in the context of distributed streaming can be transformed into distributed algorithms for model counting. We next turn our attention to viewing streaming from the lens of counting and show that framingF₀estimation as a special case of #DNF counting allows us to obtain a general recipe for a rich class of streaming problems, which had been subjected to case-specific analysis in prior works. In particular, our view yields an algorithm for multidimensional range efficientF₀estimation with a simpler analysis.

    

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2. Model Counting meets $F_0$ Estimation

   Pavan, A. ; Vinodchandran, N. V. ; Meel, Bhattacharya ; Meel, Kuldeep ( July 2021 , Proceedings of the ACM SIGACTSIGMODSIGART Symposium on Principles of Database Systems)

   null (Ed.)

   Constraint satisfaction problems (CSP's) and data stream models are two powerful abstractions to capture a wide variety of problems arising in different domains of computer science. Developments in the two communities have mostly occurred independently and with little interaction between them. In this work, we seek to investigate whether bridging the seeming communication gap between the two communities may pave the way to richer fundamental insights. To this end, we focus on two foundational problems: model counting for CSP's and computation of zeroth frequency moments $(F_0)$ for data streams. Our investigations lead us to observe striking similarity in the core techniques employed in the algorithmic frameworks that have evolved separately for model counting and $F_0$ computation. We design a recipe for translation of algorithms developed for $F_0$ estimation to that of model counting, resulting in new algorithms for model counting. We then observe that algorithms in the context of distributed streaming can be transformed to distributed algorithms for model counting. We next turn our attention to viewing streaming from the lens of counting and show that framing $F_0$ estimation as a special case of DNF counting allows us to obtain a general recipe for a rich class of streaming problems, which had been subjected to case-specific analysis in prior works. In particular, our view yields a state-of-the art algorithm for multidimensional range efficient $F_0$ estimation with a simpler analysis. 

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3. Model Counting Meets Distinct Elements in a Data Stream

   https://doi.org/10.1145/3542700.3542721  

   Pavan, A. ; Vinodchandran, N. V. ; Bhattacharyya, Arnab ; Meel, Kuldeep S. ( May 2022 , ACM SIGMOD Record)

   Constraint satisfaction problems (CSPs) and data stream models are two powerful abstractions to capture a wide variety of problems arising in different domains of computer science. Developments in the two communities have mostly occurred independently and with little interaction between them. In this work, we seek to investigate whether bridging the seeming communication gap between the two communities may pave the way to richer fundamental insights. To this end, we focus on two foundational problems: model counting for CSPs and computation of zeroth frequency moments (F0) for data streams. 

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4. Triangle and Four Cycle Counting with Predictions in Graph Streams

   Chen, J. ; Eden, T. ; Indyk, P. ; Narayanan, S. ; Rubinfeld, R. ; Silwal, S. ; Woodruff, D. ; Zhang, M. ( January 2022 , Tenth International Conference on Learning Representations (ICLR 2022))

   We propose data-driven one-pass streaming algorithms for estimating the number of triangles and four cycles, two fundamental problems in graph analytics that are widely studied in the graph data stream literature. Recently, Hsu et al. (2019a) and Jiang et al. (2020) applied machine learning techniques in other data stream problems, using a trained oracle that can predict certain properties of the stream elements to improve on prior “classical” algorithms that did not use oracles. In this paper, we explore the power of a “heavy edge” oracle in multiple graph edge streaming models. In the adjacency list model, we present a one-pass triangle counting algorithm improving upon the previous space upper bounds without such an oracle. In the arbitrary order model, we present algorithms for both triangle and four cycle estimation with fewer passes and the same space complexity as in previous algorithms, and we show several of these bounds are optimal. We analyze our algorithms under several noise models, showing that the algorithms perform well even when the oracle errs. Our methodology expands upon prior work on “classical” streaming algorithms, as previous multi-pass and random order streaming algorithms can be seen as special cases of our algorithms, where the first pass or random order was used to implement the heavy edge oracle. Lastly, our experiments demonstrate advantages of the proposed method compared to state-of-the-art streaming algorithms. 

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5. A Framework for Adversarially Robust Streaming Algorithms

   https://doi.org/10.1145/3498334  

   Ben-Eliezer, Omri ; Jayaram, Rajesh ; Woodruff, David P. ; Yogev, Eylon ( April 2022 , Journal of the ACM)

   We investigate the adversarial robustness of streaming algorithms. In this context, an algorithm is considered robust if its performance guarantees hold even if the stream is chosen adaptively by an adversary that observes the outputs of the algorithm along the stream and can react in an online manner. While deterministic streaming algorithms are inherently robust, many central problems in the streaming literature do not admit sublinear-space deterministic algorithms; on the other hand, classical space-efficient randomized algorithms for these problems are generally not adversarially robust. This raises the natural question of whether there exist efficient adversarially robust (randomized) streaming algorithms for these problems. In this work, we show that the answer is positive for various important streaming problems in the insertion-only model, including distinct elements and more generally F p -estimation, F p -heavy hitters, entropy estimation, and others. For all of these problems, we develop adversarially robust (1+ε)-approximation algorithms whose required space matches that of the best known non-robust algorithms up to a poly(log n , 1/ε) multiplicative factor (and in some cases even up to a constant factor). Towards this end, we develop several generic tools allowing one to efficiently transform a non-robust streaming algorithm into a robust one in various scenarios. 

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