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1. Strong Consistency, Graph Laplacians, and the Stochastic Block Model

   Deng, Shaofeng; Ling, Shuyang; Strohmer, Thomas (May 2021, Journal of machine learning research)

   Spectral clustering has become one of the most popular algorithms in data clustering and community detection. We study the performance of classical two-step spectral clustering via the graph Laplacian to learn the stochastic block model. Our aim is to answer the following question: when is spectral clustering via the graph Laplacian able to achieve strong consistency, i.e., the exact recovery of the underlying hidden communities? Our work provides an entrywise analysis (an ℓ∞-norm perturbation bound) of the Fiedler eigenvector of both the unnormalized and the normalized Laplacian associated with the adjacency matrix sampled from the stochastic block model. We prove that spectral clustering is able to achieve exact recovery of the planted community structure under conditions that match the information-theoretic limits. 

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2. "What Do Your Friends Think?": Efficient Polling Methods for Networks Using Friendship Paradox

   https://doi.org/10.1109/TKDE.2019.2940914  

   Nettasinghe, Buddhika; Krishnamurthy, Vikram (September 2019, IEEE Transactions on Knowledge and Data Engineering)

   This paper deals with randomized polling of a social network. In the case of forecasting the outcome of an election between two candidates A and B, classical intent polling asks randomly sampled individuals: who will you vote for? Expectation polling asks: who do you think will win? In this paper, we propose a novel neighborhood expectation polling (NEP) strategy that asks randomly sampled individuals: what is your estimate of the fraction of votes for A? Therefore, in NEP, sampled individuals will naturally look at their neighbors (defined by the underlying social network graph) when answering this question. Hence, the mean squared error (MSE) of NEP methods rely on selecting the optimal set of samples from the network. To this end, we propose three NEP algorithms for the following cases: (i) the social network graph is not known but, random walks (sequential exploration) can be performed on the graph (ii) the social network graph is unknown. For case (i) and (ii), two algorithms based on a graph theoretic consequence called friendship paradox are proposed. Theoretical results on the dependence of the MSE of the algorithms on the properties of the network are established. Numerical results on real and synthetic data sets are provided to illustrate the performance of the algorithms. 

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3. HLPerf: Demystifying the Performance of HLS-based Graph Neural Networks with Dataflow Architectures

   https://doi.org/10.1145/3655627  

   Zhao, Chenfeng; Faber, Clayton J.; Chamberlain, Roger D.; Zhang, Xuan (April 2024, ACM Transactions on Reconfigurable Technology and Systems)

   The development of FPGA-based applications using HLS is fraught with performance pitfalls and large design space exploration times. These issues are exacerbated when the application is complicated and its performance is dependent on the input data set, as is often the case with graph neural network approaches to machine learning. Here, we introduce HLPerf, an open-source, simulation-based performance evaluation framework for dataflow architectures that both supports early exploration of the design space and shortens the performance evaluation cycle. We apply the methodology to GNNHLS, an HLS-based graph neural network benchmark containing 6 commonly used graph neural network models and 4 datasets with distinct topologies and scales. The results show that HLPerf achieves over 10 000 × average simulation acceleration relative to RTL simulation and over 400 × acceleration relative to state-of-the-art cycle-accurate tools at the cost of 7% mean error rate relative to actual FPGA implementation performance. This acceleration positions HLPerf as a viable component in the design cycle. 

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4. Information-Theoretic Topology-Hiding Broadcast: Wheels, Stars, Friendship, and Beyond

   https://doi.org/10.4230/LIPIcs.ITC.2024.1  

   Banoun, D'or; Boyle, Elette; Cohen, Ran (January 2024, ITC)

   Aggarwal, Divesh (Ed.)

   Topology-hiding broadcast (THB) enables parties communicating over an incomplete network to broadcast messages while hiding the network topology from within a given class of graphs. Although broadcast is a privacy-free task, it is known that THB for certain graph classes necessitates computational assumptions, even against "honest but curious" adversaries, and even given a single corrupted party. Recent works have tried to understand when THB can be obtained with information-theoretic (IT) security (without cryptography or setup assumptions) as a function of properties of the corresponding graph class. We revisit this question through a case study of the class of wheel graphs and their subgraphs. The nth wheel graph is established by connecting n nodes who form a cycle with another "center" node, thus providing a natural extension that captures and enriches previously studied graph classes in the setting of IT-THB. We present a series of new findings in this line. We fully characterize feasibility of IT-THB for any class of subgraphs of the wheel, each possessing an embedded star (i.e., a well-defined center connected to all other nodes). Our characterization provides evidence that IT-THB feasibility may correlate with a more fine-grained degree structure - as opposed to pure connectivity - of the corresponding graphs. We provide positive results achieving perfect IT-THB for new graph classes, including ones where the number of nodes is unknown. Further, we provide the first feasibility of IT-THB on non-degenerate graph-classes with t > 1 corruptions, for the class of friendship graphs (Erdös, Rényi, Sós '66). 

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5. Phase-type bounds on network performance

   https://doi.org/10.1109/CISS.2018.8362284  

   Boroujeny, Massieh Kordi; Ephraim, Yariv; Mark, Brian L. (March 2018, 52nd Annual Conference on Information Sciences and Systems (CISS))

   Evaluation of end-to-end network performance using realistic traffic models is a challenging problem in networking. The classical theory of queueing networks is feasible only under rather restrictive assumptions on the input traffic models and network elements. An alternative approach, first proposed in the late 1980s, is to impose deterministic bounds on the input traffic that can be used as a basis for a network calculus to compute end-to-end network delay bounds. Such deterministic bounds are inherently loose as they must accommodate worst case scenarios. Since the early 1990s, efforts have shifted to development of a stochastic network calculus to provide probabilistic end-to-end performance bounds. In this paper, we capitalize on the approach of stochastically bounded burstiness (SBB) which was developed for a general class of bounding functions, and was demonstrated for a bound that is based on a mixture distribution. We specialize the SBB bounds to bounds based on the class of phase-type distributions, which includes mixture distributions as a particular case. We develop the phase-type bounds and demonstrate their performance. 

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