In this paper, we derive a class of step-size rules (time-varying gains) for gradient-based extremum seeking algorithms that guarantee classical asymptotic convergence rather than practical convergence. The obtained s...
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In this paper, we derive a class of step-size rules (time-varying gains) for gradient-based extremum seeking algorithms that guarantee classical asymptotic convergence rather than practical convergence. The obtained step-size rule conditions are similar to the classical step-size rules known in stochastic approximation theory.
Given a set of clients and a set of facilities with different priority levels in a metric space, the BUDGETED PRIORITY p-MEDIAN problem aims to open a subset of facilities and connect each client to an opened facility...
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Given a set of clients and a set of facilities with different priority levels in a metric space, the BUDGETED PRIORITY p-MEDIAN problem aims to open a subset of facilities and connect each client to an opened facility with the same or a higher priority level, such that the number of opened facilities associated with each priority level is no more than a given upper limit, and the sum of the client-connection costs is minimized. In this paper, we present a data reduction-based approach for limiting the solution search space of the BUDGETED PRIORITY p-MEDIAN problem, which yields a (1+epsilon)-approximation algorithm running in O(nd log n) + (p epsilon(-1))(p epsilon-O(1))n(O(1)) time in d-dimensional Euclidean space, where n is the size of the input instance and p is the maximal number of opened facilities. The previous best approximation ratio for this problem obtained in the same time is (3 + epsilon).
In the reconciliation k-median problem we ask to cluster a set of data points by picking k cluster centers so as to minimize the sum of distances of the data points to their cluster centers plus the sum of pairwise di...
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In the reconciliation k-median problem we ask to cluster a set of data points by picking k cluster centers so as to minimize the sum of distances of the data points to their cluster centers plus the sum of pairwise distances between the centers. The problem, which is a variant of classic k-median, aims to find a set of cluster centers that are not too far from each other, and it has applications, for example, when selecting a committee to deliberate on a controversial topic. This problem was introduced recently (Ordozgoiti and Gionis, 2019), and it was shown that a local-search-based algorithm is always within a factor O(k) of an optimum solution and performs well in practice. In this paper, we demonstrate a close connection of reconciliation k-median to a variant of the k-facility location problem, in which each potential cluster center has an individual opening cost and we aim at minimizing the sum of client-center distances and the opening costs. This connection enables us to provide a new algorithm for reconciliation k-median that yields a constant-factor approximation (independent of k). We also provide a sparsification scheme that reduces the number of potential cluster centers to O(k) in order to substantially speed up approximation algorithms. We empirically compare our new algorithms with the previous local-search approach, showing improved performance and stability. In addition, we show how our sparsification approach helps to reduce computation time without significantly compromising the solution quality.
A study of the possibilities of measuring current values, phase shift angles and other parameters of electrical networks using these data, when sampling with a frequency not multiple of the network frequency, was carr...
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This letter propose a quasi-Newton based weighted minimum mean square error (WMMSE) algorithm without matrix inverse to solve the weighted sum rate (WSR) maximization problem in multi-user multi-input single-output (M...
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This letter propose a quasi-Newton based weighted minimum mean square error (WMMSE) algorithm without matrix inverse to solve the weighted sum rate (WSR) maximization problem in multi-user multi-input single-output (MU-MISO) beamforming. On one hand, the quasi-Newton method can replace the first-order optimal condition to solve the extremum problem of the convex quadratic function, without involving matrix inverse. One the other hand, compared to projected gradient descent (PGD) approach, it can achieve a faster convergence under the guidance of approximate Hessian matrix and avoid performance loss under the condition of high transmit power. Furthermore, a learning strategy is adopted to replace the linear searching process to obtain the optimal step size that satisfies the Wolfe condition. Simulation results validate that the proposed algorithm can achieve the same performance as WMMSE, but with a reduced computation complexity.
In this article, we consider using time-of-arrival (TOA) measurements from a single moving receiver to locate a moving target at constant velocity that emits a periodic signal with unknown signal period. First, we giv...
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In this article, we consider using time-of-arrival (TOA) measurements from a single moving receiver to locate a moving target at constant velocity that emits a periodic signal with unknown signal period. First, we give the TOA measurement model and deduce the Cram e r-Rao lower bounds (CRLB). Then, we formulate a nonlinear least squares (NLS) problem to estimate the unknown parameters. We use semidefinite programming (SDP) techniques to relax the nonconvex NLS problem. However, it is shown that the SDP localization algorithm cannot provide a high-quality solution. Subsequently, we develop a fixed point iteration (FPI) method to improve the performance of the SDP algorithm. In addition, we also consider the presence of receiver position errors and develop the corresponding localization algorithm. Numerical simulations are conducted to demonstrate the localization performance of the proposed algorithms by comparing them with the CRLB. Index Term-Fixed point iteration (FPI), semidefinite programming (SDP), single moving receiver, target localization, time-of-arrival (TOA).
The Connected Sensor Problem(CSP)presents a prevalent challenge in the realms of communication and Internet of Things(IoT)*** primary aim is to maximize the coverage of users while maintaining connectivity among K ***...
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The Connected Sensor Problem(CSP)presents a prevalent challenge in the realms of communication and Internet of Things(IoT)*** primary aim is to maximize the coverage of users while maintaining connectivity among K *** the challenge of managing a large user base alongside a finite number of candidate locations,this paper proposes an extension to the CSP:the h-hop independently submodular maximization problem characterized by curvatureα.We have developed an approximation algorithm that achieves a ratio of 1−e−α/(2h+3)α.The efficacy of this algorithm is demonstrated on the CSP,where it shows superior performance over existing algorithms,marked by an average enhancement of 8.4%.
We present dynamic algorithms with polylogarithmic update time for estimating the size of the maximum matching of a graph undergoing edge insertions and deletions with approximation ratio strictly better than 2. Speci...
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ISBN:
(纸本)9781611977554
We present dynamic algorithms with polylogarithmic update time for estimating the size of the maximum matching of a graph undergoing edge insertions and deletions with approximation ratio strictly better than 2. Specifically, we obtain a 1 + root 1/2 + epsilon approximate to 1.707+epsilon approximation in bipartite graphs and a 1.973+epsilon approximation in general graphs. We thus answer in the affirmative the value version of the major open question repeatedly asked in the dynamic graph algorithms literature. Our randomized algorithms' approximation and worst-case update time bounds both hold w.h.p. against adaptive adversaries. Our algorithms are based on simulating new two-pass streaming matching algorithms in the dynamic setting. Our key new idea is to invoke the recent sublinear-time matching algorithm of Behnezhad (FOCS'21) in a white-box manner to efficiently simulate the second pass of our streaming algorithms, while bypassing the well-known vertex-update barrier.
In this letter, a low-complexity demodulation algorithm for amplify-and-forward (AF) barrage relay networks (BRN) has been proposed, which is based on approximate message passing (AMP) algorithm. Different from previo...
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In this letter, a low-complexity demodulation algorithm for amplify-and-forward (AF) barrage relay networks (BRN) has been proposed, which is based on approximate message passing (AMP) algorithm. Different from previous research, the delay for each relay node has been added in our established channel model of BRN, which is more suitable for practical applications. Then, by simplifying the expression of maximum a posterior probability, we have proposed the AF-AMP demodulation algorithm for BRN, and analyzed its computational complexity. Simulation results demonstrate that our proposed algorithm has lower complexity.
Average consensus is a cornerstone of distributed systems, facilitating essential functionalities such as distributed information fusion, decision-making, and decentralized control. However, achieving the exact averag...
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Average consensus is a cornerstone of distributed systems, facilitating essential functionalities such as distributed information fusion, decision-making, and decentralized control. However, achieving the exact average consensus is challenging when partial nodes are compromised and act as Byzantine attackers by transmitting malicious messages using judiciously crafted patterns. Existing resilient consensus results can only guarantee that the consensus value under Byzantine attacks remains within the range defined by the maximum and minimum initial state values of all legitimate nodes. In addition, the consensus value is highly uncertain when attack strategies change. In this letter, we propose a new resilient consensus algorithm that ensures the consensus value falls within a much tighter bound. The bound contains the exact average consensus value and is solely determined by the initial states of legitimate nodes, regardless of the attack strategies employed by the Byzantine attackers. More interestingly, we demonstrate that the bound is the tightest achievable under our resilient consensus algorithm when the number of Byzantine attackers reaches the maximum threshold our algorithm can handle. Numerical simulations are given to validate the theoretical results.
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