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1. On the Positive Effect of Delay on the Rate of Convergence of a Class of Linear Time-Delayed Systems

   https://doi.org/10.1109/TAC.2019.2961348  

   Moradian, Hossein; Kia, Solmaz S. (January 2020, IEEE Transactions on Automatic Control)

   This paper is a comprehensive study of a long-observed phenomenon of an increase in the stability margin and so the rate of convergence of a class of linear systems due to time delay. We use Lambert W function to determine (a) in what systems the delay can lead to increase in the rate of convergence, (b) the exact range of time delay for which the rate of convergence is greater than that of the delay-free system, and (c) an estimate on the value of the delay that leads to the maximum rate of convergence. For the special case when the system matrix eigenvalues are all negative real numbers, we expand our results to show that the rate of convergence in the presence of delay depends only on the eigenvalues with minimum and maximum real parts. Moreover, we determine the exact value of the maximum rate of convergence and the corresponding maximizing time delay. We demonstrate our results through a numerical example on the practical application in accelerating an agreement algorithm for networked~systems by use of delayed feedback. 

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2. SEAFL: Enhancing Efficiency in Semi-Asynchronous Federated Learning Through Adaptive Aggregation and Selective Training

   https://doi.org/10.1109/IPDPS64566.2025.00052  

   Islam, Md Sirajul; Panta, Sanjeev; Xu, Fei; Yuan, Xu; Chen, Li; Tzeng, Nian-Feng (June 2025, IEEE International Parallel & Distributed Processing Symposium (IPDPS 2025))

   Federated Learning (FL) is a promising distributed machine learning framework that allows collaborative learning of a global model across decentralized devices without uploading their local data. However, in real-world FL scenarios, the conventional synchronous FL mechanism suffers from inefficient training caused by slow-speed devices, commonly known as stragglers, especially in heterogeneous communication environments. Though asynchronous FL effectively tackles the efficiency challenge, it induces substantial system overheads and model degradation. Striking for a balance, semi-asynchronous FL has gained increasing attention, while still suffering from the open challenge of stale models, where newly arrived updates are calculated based on outdated weights that easily hurt the convergence of the global model. In this paper, we present SEAFL, a novel FL framework designed to mitigate both the straggler and the stale model challenges in semi-asynchronous FL. SEAFL dynamically assigns weights to uploaded models during aggregation based on their staleness and importance to the current global model. We theoretically analyze the convergence rate of SEAFL and further enhance the training efficiency with an extended variant that allows partial training on slower devices, enabling them to contribute to global aggregation while reducing excessive waiting times. We evaluate the effectiveness of SEAFL through extensive experiments on three benchmark datasets. The experimental results demonstrate that SEAFL outperforms its closest counterpart by up to ∼22% in terms of the wall-clock training time required to achieve target accuracy. 

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3. A Parallel 2/3-Approximation Algorithm for Vertex-Weighted Matching

   https://doi.org/10.1137/1.9781611976229.2  

   Al-Herz, Ahmed; Pothen, Alex (January 2020, SIAM 2020 Workshop on Combinatorial Scientific Computing)

   We consider the maximum vertex-weighted matching problem (MVM), in which non-negative weights are assigned to the vertices of a graph, and the weight of a matching is the sum of the weights of the matched vertices. Although exact algorithms for MVM are faster than exact algorithms for the maximum edge-weighted matching problem, there are graphs on which these exact algorithms could take hundreds of hours. For a natural number k, we design a k/(k + 1)approximation algorithm for MVM on non-bipartite graphs that updates the matching along certain short paths in the graph: either augmenting paths of length at most 2k + 1 or weight-increasing paths of length at most 2k. The choice of k = 2 leads to a 2/3-approximation algorithm that computes nearly optimal weights fast. This algorithm could be initialized with a 2/3-approximate maximum cardinality matching to reduce its runtime in practice. A 1/2-approximation algorithm may be obtained using k = 1, which is faster than the 2/3-approximation algorithm but it computes lower weights. The 2/3-approximation algorithm has time complexity O(Δ2m) while the time complexity of the 1/2-approximation algorithm is O(Δm), where m is the number of edges and Δ is the maximum degree of a vertex. Results from our serial implementations show that on average the 1/2-approximation algorithm runs faster than the Suitor algorithm (currently the fastest 1/2-approximation algorithm) while the 2/3-approximation algorithm runs as fast as the Suitor algorithm but obtains higher weights for the matching. One advantage of the proposed algorithms is that they are well-suited for parallel implementation since they can process vertices to match in any order. The 1/2- and 2/3-approximation algorithms have been implemented on a shared memory parallel computer, and both approximation algorithms obtain good speedups, while the former algorithm runs faster on average than the parallel Suitor algorithm. Care is needed to design the parallel algorithm to avoid cyclic waits, and we prove that it is live-lock free. 

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4. Convergence Analysis for an Online Data-Driven Feedback Control Algorithm

   https://doi.org/10.3390/math12162584  

   Liang, Siming; Sun, Hui; Archibald, Richard; Bao, Feng (August 2024, Mathematics)

   This paper presents convergence analysis of a novel data-driven feedback control algorithm designed for generating online controls based on partial noisy observational data. The algorithm comprises a particle filter-enabled state estimation component, estimating the controlled system’s state via indirect observations, alongside an efficient stochastic maximum principle-type optimal control solver. By integrating weak convergence techniques for the particle filter with convergence analysis for the stochastic maximum principle control solver, we derive a weak convergence result for the optimization procedure in search of optimal data-driven feedback control. Numerical experiments are performed to validate the theoretical findings. 

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5. A Weighted Approach to the Maximum Cardinality Bipartite Matching Problem with Applications in Geometric Settings

   Lahn, Nathaniel; Raghvendra, Sharath (June 2019, Leibniz international proceedings in informatics)

   We present a weighted approach to compute a maximum cardinality matching in an arbitrary bipartite graph. Our main result is a new algorithm that takes as input a weighted bipartite graph G(A cup B,E) with edge weights of 0 or 1. Let w <= n be an upper bound on the weight of any matching in G. Consider the subgraph induced by all the edges of G with a weight 0. Suppose every connected component in this subgraph has O(r) vertices and O(mr/n) edges. We present an algorithm to compute a maximum cardinality matching in G in O~(m(sqrt{w} + sqrt{r} + wr/n)) time. When all the edge weights are 1 (symmetrically when all weights are 0), our algorithm will be identical to the well-known Hopcroft-Karp (HK) algorithm, which runs in O(m sqrt{n}) time. However, if we can carefully assign weights of 0 and 1 on its edges such that both w and r are sub-linear in n and wr=O(n^{gamma}) for gamma < 3/2, then we can compute maximum cardinality matching in G in o(m sqrt{n}) time. Using our algorithm, we obtain a new O~(n^{4/3}/epsilon^4) time algorithm to compute an epsilon-approximate bottleneck matching of A,B subsetR^2 and an 1/(epsilon^{O(d)}}n^{1+(d-1)/(2d-1)}) poly log n time algorithm for computing epsilon-approximate bottleneck matching in d-dimensions. All previous algorithms take Omega(n^{3/2}) time. Given any graph G(A cup B,E) that has an easily computable balanced vertex separator for every subgraph G'(V',E') of size |V'|^{delta}, for delta in [1/2,1), we can apply our algorithm to compute a maximum matching in O~(mn^{delta/1+delta}) time improving upon the O(m sqrt{n}) time taken by the HK-Algorithm. 

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