In this paper, we develop a kernel-independent and purely algebraic method, Nested Pseudo-Skeleton approximation (NPSA) algorithm, to generate a low-rank H-2-matrix representation of electrically large surface integra...
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In this paper, we develop a kernel-independent and purely algebraic method, Nested Pseudo-Skeleton approximation (NPSA) algorithm, to generate a low-rank H-2-matrix representation of electrically large surface integral equations (SIEs). The algorithm only uses O(NlogN) entries of the original dense SIE matrix of size N to generate the H-2-representation. It also provides a closed-form expression of the cluster bases and coupling matrices with respect to original matrix entries. The resultant H-2-matrix is then directly solved for electrically large scattering analysis. Numerical experiments have demonstrated the accuracy and efficiency of the proposed algorithm. In addition to surface integral equations, the proposed algorithms can also be applied to solving other electrically large integral equations.
Column selection is an essential tool for structure-preserving low-rank approximation, with wide-ranging applications across many fields, such as data science, machine learning, and theoretical chemistry. In this work...
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Given a graph G(N,A) with a cost (or benefit) and a delay on each arc, the constrained routing problem (CRP) aims to find a minimum-cost or a maximum-benefit path from a given source to a given destination node, subje...
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Given a graph G(N,A) with a cost (or benefit) and a delay on each arc, the constrained routing problem (CRP) aims to find a minimum-cost or a maximum-benefit path from a given source to a given destination node, subject to an end-to-end delay constraint. The problem (with a single constraint) is NP-hard, and has been studied by many researchers who found fully polynomial approximation schemes (FPAS) for this problem. The current paper focuses on a generalized CRP version, CRP with hop-wise constraints (CRPH). In the generalized version, instead of one constraint there are up to n-1 special-type constraints, where n is the number of nodes. An FPAS based on interval partitioning is proposed for both the minimization and the maximization versions of CRPH. For G(N,A) with n nodes and m arcs, the complexity of the algorithm is O(mn (2)/epsilon).
Abstract: This paper aims to solve a solid transportation problem, wherein the uncertain parameters related to the problem are represented using triangular Fermatean fuzzy numbers. Fermatean fuzzy sets offer a relativ...
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This letter investigates the problem of output tracking control subject to transient and steady-state performance constraints for unknown pure-feedback systems. On the basis of monotonicity theory, we propose a univer...
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This letter investigates the problem of output tracking control subject to transient and steady-state performance constraints for unknown pure-feedback systems. On the basis of monotonicity theory, we propose a universal mapping-based barrier Lyapunov function (MBLF) which addresses the performance constraints without any sign limitation. Then an approximation-free controller is derived via the joint use of backstepping technique and MBLF. Through the Lyapunov stability analysis, it is proved that this controller can stabilize all the closed-loop signals including MBLF, and moreover the prescribed output tracking is achieved under a naturally satisfied initial virtual condition, and without any sacrifice of output overshoot performance. In the end, a simulation example is provided to demonstrate the effectiveness of the proposed scheme, and also the superiority over the existing ones.
Computing optimal subset repairs and optimal update repairs of an inconsistent database has a wide range of applications and is becoming standalone research problems. However, these problems have not been well studied...
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Computing optimal subset repairs and optimal update repairs of an inconsistent database has a wide range of applications and is becoming standalone research problems. However, these problems have not been well studied in terms of both inapproximability and approximation algorithms. In this paper, we prove a new tighter inapproximability bound for computing optimal subset repairs. We show that it is frequently NP-hard to approximate an optimal subset repair within a factor better than 143/136. We develop an algorithm for computing optimal subset repairs with an approximation ratio (2 - 1/2(sigma-1)), where sigma is the number of functional dependencies. We improve it when the database contains a large amount of quasi-Turan clusters. We then extend our work for computing optimal update repairs. We show it is NP-hard to approximate an optimal update repair within a factor better than 143/136 for representative cases. We further develop an approximation algorithm for computing optimal update repairs with an approximation ratio mlc(Sigma)(2 - 1/2(sigma)(-1)), where mlc( E) depends on the given functional dependencies. We conduct experiments on real data to examine the performance and the effectiveness of our proposed approximation algorithms
In the multiway cut problem we are given a weighted undirected graph G = (V, E) and a set T & SUBE;V of k terminals. The goal is to find a minimum weight set of edges E & PRIME;& SUBE;E with the property t...
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In the multiway cut problem we are given a weighted undirected graph G = (V, E) and a set T & SUBE;V of k terminals. The goal is to find a minimum weight set of edges E & PRIME;& SUBE;E with the property that by removing E & PRIME;from G all the terminals become disconnected. In this paper we present a simple local search approximation algorithm for the multiway cut problem with approximation ratio 2 - k2. We present an experimental evaluation of the performance of our local search algorithm and show that it greatly outperforms the isolation heuristic of Dalhaus et al. and it has similar performance as the much more complex algorithms of Calinescu et al., Sharma and Vondrak, and Buchbinder et al. which have the currently best known approximation ratios for this problem.& COPY;2023 Elsevier B.V. All rights reserved.
We present a new approximation algorithm for the minimum 2-edge-connected spanning subgraph problem. Its approximation ratio is 43 , which matches the current best ratio. The approximation ratio of the algorithm is s ...
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We present a new approximation algorithm for the minimum 2-edge-connected spanning subgraph problem. Its approximation ratio is 43 , which matches the current best ratio. The approximation ratio of the algorithm is s on subcubic graphs, which is an improvement upon the previous best ratio of 54. The algorithm is a novel extension of the primal-dual schema, which consists of two distinct phases. Both the algorithm and the analysis are much simpler than those of the previous approaches.(c) 2022 Elsevier B.V. All rights reserved.
Given cell-average data values of a piecewise-smooth bivariate function f within a domain Omega, we look for a piecewise adaptive approximation to f. We are interested in an explicit and global (smooth) approach. Biva...
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Given cell-average data values of a piecewise-smooth bivariate function f within a domain Omega, we look for a piecewise adaptive approximation to f. We are interested in an explicit and global (smooth) approach. Bivariate approximation techniques, as trigonometric or splines approximations, achieve reduced approximation orders near the boundary of the domain and near curves of jump singularities of the function or its derivatives. Whereas the boundary of Omega is assumed to be known, the subdivision of Omega to subdomains on which f is smooth is unknown. The first challenge of the proposed approximation algorithm would be to find a good approximation to the curves separating the smooth subdomains of f. In the second stage, we simultaneously look for approximations to the different smooth segments of f, where on each segment we approximate the function by a linear combination of basis functions {p(i)}(i=1)(M), considering the corresponding cell averages. A discrete Laplacian operator applied to the given cell-average data intensifies the structure of the singularity of the data across the curves separating the smooth subdomains of f. We refer to these derived values as the signature of the data, and we use it for both approximating the singularity curves separating the different smooth regions off . The main contributions here are improved convergence rates to the approximation of the singularity curves and the approximation of f, an explicit and global formula, and, in particular, the derivation of a piecewise-smooth high-order approximation to the function.
In this article, a distributed smoothing accelerated projection algorithm (DSAPA) is proposed to address constrained nonsmooth convex optimization problems over undirected multiagent networks in a distributed manner, ...
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In this article, a distributed smoothing accelerated projection algorithm (DSAPA) is proposed to address constrained nonsmooth convex optimization problems over undirected multiagent networks in a distributed manner, where the objective function is free of the assumption of the Lipschitz gradient or strong convexity. First, based on a distributed exact penalty method, the original optimization problem is translated to a problem of standard assignment without consensus constraints. Then, a novel DSAPA by combining the smoothing approximation with Nesterov's accelerated schemes, is proposed. In addition, we provide a systematic analysis to derive an upper bound on the convergence rate in terms of the objective function based on penalty function and to choose the optimal step size accordingly. Our results demonstrate that the proposed DSAPA can reach $O({\log (k)}/{k})$ when the optimal step size is chosen. Finally, the effectiveness and correctness of the proposed algorithm are verified by numerical and practical application examples.
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