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1. Node-Asynchronous Implementation of Filter Banks on Graphs

   https://doi.org/10.1109/IEEECONF51394.2020.9443349  

   Teke, Oguzhan ; Vaidyanathan, P. P. ( November 2020 , Proc. Asil. Conf. Sig., Sys., and Comp)

   null (Ed.)

   Filter banks on graphs are shown to be useful for analyzing data defined over networks, as they decompose a graph signal into components with low variation and high variation. Based on recent node-asynchronous implementation of graph filters, this study proposes an asynchronous implementation of filter banks on graphs. In the proposed algorithm nodes follow a randomized collect-compute-broadcast scheme: if a node is in the passive stage it collects the data sent by its incoming neighbors and stores only the most recent data. When a node gets into the active stage at a random time instance, it does the necessary filtering computations locally, and broadcasts a state vector to its outgoing neighbors. When the underlying filters (of the filter bank) are rational functions with the same denominator, the proposed filter bank implementation does not require additional communication between the neighboring nodes. However, computations done by a node increase linearly with the number of filters in the bank. It is also proven that the proposed asynchronous implementation converges to the desired output of the filter bank in the mean-squared sense under mild stability conditions. The convergence is verified also with numerical experiments. 

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2. Iterative Chebyshev Polynomial Algorithm for Signal Denoising on Graphs

   Cheng, Cheng ; Jiang, Junzheng ; Emirov, Nazar ; Sun, Qiyu ( July 2019 , Proceeding of SampTA 2019)

   In this paper, we consider the inverse graph filtering process when the original filter is a polynomial of some graph shift on a simple connected graph. The Chebyshev polynomial approximation of high order has been widely used to approximate the inverse filter. In this paper, we propose an iterative Chebyshev polynomial approximation (ICPA) algorithm to implement the inverse filtering procedure, which is feasible to eliminate the restoration error even using Chebyshev polynomial approximation of lower order. We also provide a detailed convergence analysis for the ICPA algorithm and a distributed implementation of the ICPA algorithm on a spatially distributed network. Numerical results are included to demonstrate the satisfactory performance of the ICPA algorithm in graph signal denoising. 

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3. Contour Algorithm for Connectivity

   Du, Zhihui ; Alvarado Rodriguez, Oliver ; Li, Fuhuan ; Dindoost, Mohammad ; Bader, David ( December 2023 , The 30th IEEE International Conference on High Performance Computing, Data, and Analytics (HiPC))

   Finding connected components in a graph is a fundamental problem in graph analysis. In this work, we present a novel minimum-mapping based Contour algorithm to efficiently solve the connectivity problem. We prove that the Contour algorithm with two or higher order operators can identify all connected components of an undirected graph within O(log d_max) iterations, with each iteration involving O(m) work, where d_max represents the largest diameter among all components in the given graph, and m is the total number of edges in the graph. Importantly, each iteration is highly parallelizable, making use of the efficient minimum-mapping operator applied to all edges. To further enhance its practical performance, we optimize the Contour algorithm through asynchronous updates, early convergence checking, eliminating atomic operations, and choosing more efficient mapping operators. Our implementation of the Contour algorithm has been integrated into the open-source framework Arachne. Arachne extends Arkouda for large-scale interactive graph analytics, providing a Python API powered by the high-productivity parallel language Chapel. Experimental results on both real-world and synthetic graphs demonstrate the superior performance of our proposed Contour algorithm compared to state-of-the-art large-scale parallel algorithm FastSV and the fastest shared memory algorithm ConnectIt. On average, Contour achieves a speedup of 7.3x and 1.4x compared to FastSV and ConnectIt, respectively. All code for the Contour algorithm and the Arachne framework is publicly available on GitHub {https://github.com/Bears-R-Us/arkouda-njit), ensuring transparency and reproducibility of our work. 

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4. Can We Break Symmetry with o(m) Communication?

   https://doi.org/10.1145/3465084  

   Pai, Shreyas ; Pandurangan, Gopal ; Pemmaraju, Sriram ; Robinson, Peter ( July 2021 , PODC'21: Proceedings of the 2021 ACM Symposium on Principles of Distributed Computing)

   null (Ed.)

   We study the communication cost (or message complexity) of fundamental distributed symmetry breaking problems, namely, coloring and MIS. While significant progress has been made in understanding and improving the running time of such problems, much less is known about the message complexity of these problems. In fact, all known algorithms need at least Ω(m) communication for these problems, where m is the number of edges in the graph. We addressthe following question in this paper: can we solve problems such as coloring and MIS using sublinear, i.e., o(m) communication, and if sounder what conditions? In a classical result, Awerbuch, Goldreich, Peleg, and Vainish [JACM 1990] showed that fundamental global problems such asbroadcast and spanning tree construction require at least o(m) messages in the KT-1 Congest model (i.e., Congest model in which nodes have initial knowledge of the neighbors' ID's) when algorithms are restricted to be comparison-based (i.e., algorithms inwhich node ID's can only be compared). Thirty five years after this result, King, Kutten, and Thorup [PODC 2015] showed that onecan solve the above problems using Õ(n) messages (n is the number of nodes in the graph) in Õ(n) rounds in the KT-1 Congest model if non-comparison-based algorithms are permitted. An important implication of this result is that one can use the synchronous nature of the KT-1 Congest model, using silence to convey information,and solve any graph problem using non-comparison-based algorithms with Õ(n) messages, but this takes an exponential number of rounds. In the asynchronous model, even this is not possible. In contrast, much less is known about the message complexity of local symmetry breaking problems such as coloring and MIS. Our paper fills this gap by presenting the following results. Lower bounds: In the KT-1 CONGEST model, we show that any comparison-based algorithm, even a randomized Monte Carlo algorithm with constant success probability, requires Ω(n 2) messages in the worst case to solve either (△ + 1)-coloring or MIS, regardless of the number of rounds. We also show that Ω(n) is a lower bound on the number ofmessages for any (△ + 1)-coloring or MIS algorithm, even non-comparison-based, and even with nodes having initial knowledge of up to a constant radius. Upper bounds: In the KT-1 CONGEST model, we present the following randomized non-comparison-based algorithms for coloring that, with high probability, use o(m) messages and run in polynomially many rounds.(a) A (△ + 1)-coloring algorithm that uses Õ(n1.5) messages, while running in Õ(D + √ n) rounds, where D is the graph diameter. Our result also implies an asynchronous algorithm for (△ + 1)-coloring with the same message bound but running in Õ(n) rounds. (b) For any constantε > 0, a (1+ε)△-coloring algorithm that uses Õ(n/ε 2 ) messages, while running in Õ(n) rounds. If we increase our input knowledge slightly to radius 2, i.e.,in the KT-2 CONGEST model, we obtain:(c) A randomized comparison-based MIS algorithm that uses Õ(n 1.5) messages. while running in Õ( √n) rounds. While our lower bound results can be viewed as counterparts to the classical result of Awerbuch, Goldreich, Peleg, and Vainish [JACM 90], but for local problems, our algorithms are the first-known algorithms for coloring and MIS that take o(m) messages and run in polynomially many rounds. 

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5. An Asynchronous Multi-Agent Actor-Critic Algorithm for Distributed Reinforcement Learning

   Lin, Yixuan ; Luo, Yuehan ; Zhang, Kaiqing ; Yang, Zhuoran ; Wang, Zhaoran ; Basar, Tamer ; Sandhu, Romeil ; Liu, Ji ( January 2019 , NeurIPS Optimization Foundations for Reinforcement Learning Workshop)

   This paper studies a distributed reinforcement learning problem in which a network of multiple agents aim to cooperatively maximize the globally averaged return through communication with only local neighbors. An asynchronous multi-agent actor-critic algorithm is proposed for possibly unidirectional communication relationships depicted by a directed graph. Each agent independently updates its variables at “event times” determined by its own clock. It is not assumed that the agents’ clocks are synchronized or that the event times are evenly spaced. It is shown that the algorithm can solve the problem for any strongly connected graph in the presence of communication and computation delays. 

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