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Analytic Sensor Rules for Optimal Distributed Decision Given K-Out-of-L Fusion Rule Under Monte Carlo approximation

IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2020年第12期65卷 5488-5495页

作者： Liao, Yiwei Shen, Xiaojing Rao, Hang Sichuan Univ Sch Math Chengdu 610017 Peoples R China

With the development of large-scale sensor networks, there is an increasing interest for high dimensional distributed decision fusion problem in statistical decision, machine learning, control theory, etc. In this article, we investigate the optimal sensor quantized rules of the distributed decision under a given fusion rule for conditionally dependent and high dimensional sensor observations. We provide a Monte Carlo importance sampling method to reduce the computational complexity of the distributed decision fusion. For the K-out-of-L rule, we derive a group of analytic sensor rules based on the necessary and sufficient condition of the optimal sensor rules. In term of efficiency, it is significantly better than the traditional iterative search algorithms, such as the Riemann sum approximation iteration algorithm. The analytic solution is also a general result since it does not rely on the specific K value of the K-out-of-L rule, the specific conditional probability density function and the dimension of sensor observations. Thus, it can be applied to multisensor decision fusion problems with high dimensional dependent sensor observations. For the general fusion rules rather than the K-out-of-L rule, the Monte Carlo Gauss-Seidel algorithm is also provided. The numerical examples demonstrate the effectiveness of the analytic solution and the Monte Carlo Gauss-Seidel algorithm.

关键词： Monte Carlo methods Bayes methods Cost function approximation algorithms Computational complexity approximation methods Probability density function Decision fusion dependent observation fusion rule high dimensional observation Monte Carlo approximation

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Image Distortion Characterization due to Equivalent Monostatic approximation in Near-Field Bistatic SAR Imaging

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IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT 2020年第7期69卷 4898-4907页

作者： Manzoor, Zahra Al Qaseer, Mohammad Tayeb Donnell, Kristen M. Missouri Univ Sci & Technol Elect Engn Dept Rolla MO 65409 USA Iowa State Univ Elect Engn Dept Ames IA 50011 USA

The omega-k synthetic aperture radar (SAR) algorithm is a computationally efficient algorithm for near-field 3-D monostatic SAR imaging in nondestructive testing (NDT) applications. However, bistatic measurements are preferred in order to obtain high dynamic range, in particular when real-time imaging arrays are used. This article investigates the image distortion caused by using an equivalent monostatic imaging algorithm for bistatic measurements. Simulations and measurements at millimeter-wave frequencies in the Ka-band (26.5-40 GHz) are used to investigate the resultant image distortion. Furthermore, the image distortion is quantified through the root-mean-square (rms) error, which is calculated as a function of the bistatic transmitterreceiver separation distance, range, and noise power. Simulations and measurements are conducted for imaging using the raster scanning of a pair of antennas and for nonuniform imaging arrays. In addition, an approximate method for phase compensation is introduced to improve the image error from the monostatic approximation of bistatic measurement.

关键词： Distortion Imaging Receivers Transmitters Distortion measurement approximation algorithms Biomedical measurement Bistatic imaging configuration equivalent monostatic model image error phase-compensation method synthetic aperture radar (SAR) imaging

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Robust Beamforming for Enhancing Security in Multibeam Satellite Systems

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IEEE COMMUNICATIONS LETTERS 2021年第7期25卷 2161-2165页

作者： Zhang, Jian Lin, Min Ouyang, Jian Zhu, Wei-Ping De Cola, Tomaso Nanjing Univ Posts & Telecommun Coll Telecommun & Informat Engn Nanjing 210003 Peoples R China Concordia Univ Dept Elect & Comp Engn Montreal PQ H3G 1M8 Canada German Aerosp Ctr DLR Inst Commun & Nav D-82234 Oberpfaffenhofen Germany

This letter proposes a robust beamforming (BF) scheme to enhance physical layer security (PLS) of the downlink of a multibeam satellite system in the presence of either uncoordinated or coordinated eavesdroppers (Eves). Specifically, with knowing only the approximate locations of the Eves, we aim at maximizing the worst-case achievable secrecy rate (ASR) of the legitimate user (LU), subject to the constraints of per-antenna transmit power and quality of service (QoS) requirement of the LU. Since the optimization problem is non-convex, we first adopt the discretization method to deal with the unknown regions of the Eves and then exploit the log-sum-exp function to approximate the objective function. Afterwards, a BF method joint alternating direction method of multipliers (ADMM) with Dinkelbach iteration is presented to solve this non-convex problem. Finally, simulation results verify that our robust BF algorithm can effectively improve the security of multibeam satellite systems.

关键词： Manganese Satellites Security Quality of service Optimization Array signal processing approximation algorithms Multibeam satellite communications robust beamforming physical layer security alternating direction method of multipliers

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Secure Beamforming for Multiple Intelligent Reflecting Surfaces Aided mmWave Systems

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IEEE COMMUNICATIONS LETTERS 2021年第2期25卷 417-421页

作者： Xiu, Yue Zhao, Jun Yuen, Chau Zhang, Zhongpei Gui, Guan Univ Elect Sci & Technol China Natl Key Lab Sci & Technol Commun Chengdu 611731 Peoples R China Nanyang Technol Univ Script Lab Singapore 639798 Singapore Singapore Univ Technol & Design Inst Engn Singapore 487372 Singapore Nanjing Univ Posts & Telecommun Focus Lab Nanjing 210003 Peoples R China

In this letter, secure beamforming in a multiple intelligent reflecting surfaces (IRSs)-aided millimeter-wave (mmWave) system is investigated. In this system, the secrecy rate is maximized by controlling the on-off status of each IRS as well as optimizing the phase shift matrix of the IRSs. This problem is posed as a joint optimization problem of transmit beamforming and IRS control, whose goal is to maximize the secrecy rate under the total transmission power and unit-modulus constraints. The problem is difficult to solve optimally due to the nonconvexity of constraint conditions and coupled variables. To deal with this problem, we propose an alternating optimization (AO)-based algorithm based on successive convex approximation (SCA) and manifold optimization (MO) technologies. Numerical simulations show that the proposed AO-based algorithm can effectively improve the secrecy rate and outperforms traditional single IRS-aided scheme.

关键词： Optimization Array signal processing approximation algorithms Linear programming Electronic mail Propagation losses Millimeter wave communication Multiple intelligent reflecting surfaces millimeter-wave secrecy rate alternating optimization

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Efficient approximate analytical methods to solve Kaup-Kupershmidt (KK) equation 6

Efficient approximate analytical methods to solve Kaup-Kuper...

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6th International Symposium on Multidisciplinary Studies and Innovative Technologies, ISMSIT 2022

作者： Abdul Kadir, Sadoon M.Eid. Taha, Wafaa M. Hameed, Raed A. Jameel, Ali University of Tikrit College of Education for Pure Sciences Kirkuk Iraq University of Kirkuk College of Sciences Mathematics Department Kirkuk Iraq School of Quantitative Sciences Kedah Malaysia

ISBN: (数字)9781665470131

ISBN: (纸本)9781665470131

it is common knowledge that partial differential equations are becoming increasingly relevant in modern research and that the solutions to these equations are essential for addressing a wide variety of real-world applications. The primary objective of this study is to investigate possible approximations for solving the nonlinear Kaup-Kupershmidt (KK) problem using an efficient method known as the homotopy analysis method (HAM). HAM offers an appropriate strategy for controlling and adjusting the convergence series solution by taking advantage of the control parameter of convergence, which is an essential factor in the resolution of various mathematical problems. Including an auxiliary parameter in the procedure provides a time-saving and effective means of examining and assessing the precision of both linear and nonlinear problems. It has been explained how the convergence analysis algorithm works, and a graphical depiction of the HAM of the proposed applications has also been provided. The solutions that can be achieved using this method are efficient, straightforward, and straightforward, indicating that the HAM may be easily implemented and is a computationally quite attractive series. © 2022 IEEE.

关键词： Partial differential equations approximation algorithms Computational efficiency Standards Convergence

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Assortment Optimization under a Single Transition Choice Model

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PRODUCTION AND OPERATIONS MANAGEMENT 2021年第7期30卷 2122-2142页

作者： Nip, Kameng Wang, Zhenbo Wang, Zizhuo Xiamen Univ Sch Math Sci Xiamen 361005 Fujian Peoples R China Tsinghua Univ Dept Math Sci Beijing 100084 Peoples R China Chinese Univ Hong Kong Sch Data Sci Shenzhen 518172 Guangdong Peoples R China

In this study, we consider a new customer choice model which we call the single transition choice model. In this model, there is a universe of products and customers arrive at each product with a certain probability. If the arrived product is unavailable, then the seller can recommend a subset of available products and the customer will purchase one of the recommended products or choose not to purchase with certain transition probabilities. The distinguishing features of the model are that the seller can control which products to recommend depending on the arrived product, and each customer either purchases a product or leaves the market after one transition. We study the assortment optimization problem under this model. Particularly, we show that it is NP-Hard even if the customer can transition from each product to at most two products. Despite the computational complexity, we provide polynomial time algorithms or approximation algorithms for several special cases, such as when the customer can only transition from each product to at most a given number of products and the size of each recommended set is bounded. Our approximation algorithms are developed by invoking the submodularity arguments, or connecting the problem with maximum constraint satisfaction problem and applying randomized rounding techniques to its semidefinite programming relaxation. We also provide a tight worst-case performance bound for revenue-ordered assortments. In addition, we propose a compact mixed-integer program formulation, which is efficient for moderate size problems. Finally, we conduct numerical experiments to demonstrate the effectiveness of the proposed algorithms.

关键词： assortment optimization choice model approximation algorithms revenue‐ ordered assortment

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Package Delivery Using Drones with Restricted Movement Areas 33

Package Delivery Using Drones with Restricted Movement Areas

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33rd International Symposium on algorithms and Computation, ISAAC 2022

作者： Erlebach, Thomas Luo, Kelin Spieksma, Frits C.R. Department of Computer Science Durham University United Kingdom Institute of Computer Science Universität Bonn Germany Department of Mathematics and Computer Science Eindhoven University of Technology Netherlands

ISBN: (纸本)9783959772587

For the problem of delivering a package from a source node to a destination node in a graph using a set of drones, we study the setting where the movements of each drone are restricted to a certain subgraph of the given graph. We consider the objectives of minimizing the delivery time (problem DDT) and of minimizing the total energy consumption (problem DDC). For general graphs, we show a strong inapproximability result and a matching approximation algorithm for DDT as well as NP-hardness and a 2-approximation algorithm for DDC. For the special case of a path, we show that DDT is NP-hard if the drones have different speeds. For trees, we give optimal algorithms under the assumption that all drones have the same speed or the same energy consumption rate. The results for trees extend to arbitrary graphs if the subgraph of each drone is isometric. © Thomas Erlebach, Kelin Luo, and Frits C.R. Spieksma.

关键词： approximation algorithms

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Maximizing Sums of Non-Monotone Submodular and Linear Functions: Understanding the Unconstrained Case 30

Maximizing Sums of Non-Monotone Submodular and Linear Functi...

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30th Annual European Symposium on algorithms, ESA 2022

作者： Bodek, Kobi Feldman, Moran Department of Mathematics and Computer Science Open University of Israel Ra'anana Israel Computer Science Department University of Haifa Israel

ISBN: (纸本)9783959772471

Motivated by practical applications, recent works have considered maximization of sums of a submodular function g and a linear function . Almost all such works, to date, studied only the special case of this problem in which g is also guaranteed to be monotone. Therefore, in this paper we systematically study the simplest version of this problem in which g is allowed to be non-monotone, namely the unconstrained variant, which we term Regularized Unconstrained Submodular Maximization (RegularizedUSM). Our main algorithmic result is the first non-trivial guarantee for general RegularizedUSM. For the special case of RegularizedUSM in which the linear function is non-positive, we prove two inapproximability results, showing that the algorithmic result implied for this case by previous works is not far from optimal. Finally, we reanalyze the known Double Greedy algorithm to obtain improved guarantees for the special case of RegularizedUSM in which the linear function is non-negative;and we complement these guarantees by showing that it is not possible to obtain (1/2, 1)-approximation for this case (despite intuitive arguments suggesting that this approximation guarantee is natural). © 2022 Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. All rights reserved.

关键词： approximation algorithms

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Average Sensitivity of the Knapsack Problem 30

Average Sensitivity of the Knapsack Problem

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30th Annual European Symposium on algorithms, ESA 2022

作者： Kumabe, Soh Yoshida, Yuichi The University of Tokyo Japan National Institute of Informatics Tokyo Japan

ISBN: (纸本)9783959772471

In resource allocation, we often require that the output allocation of an algorithm is stable against input perturbation because frequent reallocation is costly and untrustworthy. Varma and Yoshida (SODA'21) formalized this requirement for algorithms as the notion of average sensitivity. Here, the average sensitivity of an algorithm on an input instance is, roughly speaking, the average size of the symmetric difference of the output for the instance and that for the instance with one item deleted, where the average is taken over the deleted item. In this work, we consider the average sensitivity of the knapsack problem, a representative example of a resource allocation problem. We first show a (1 - ϵ)-approximation algorithm for the knapsack problem with average sensitivity O(ϵ-1 log ϵ-1). Then, we complement this result by showing that any (1 - ϵ)-approximation algorithm has average sensitivity Ω(ϵ-1). As an application of our algorithm, we consider the incremental knapsack problem in the random-order setting, where the goal is to maintain a good solution while items arrive one by one in a random order. Specifically, we show that for any ϵ > 0, there exists a (1 - ϵ)-approximation algorithm with amortized recourse O(ϵ-1 log ϵ-1) and amortized update time O(log n + fϵ), where n is the total number of items and fϵ > 0 is a value depending on ϵ. © 2022 Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. All rights reserved.

关键词： approximation algorithms

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Improving the Dilation of a Metric Graph by Adding Edges

Improving the Dilation of a Metric Graph by Adding Edges

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作者： Gudmundsson, Joachim Wong, Sampson University of Sydney Building J12/1 Cleveland St CamperdownNSW2006 Australia

Most of the literature on spanners focuses on building the graph from scratch. This article instead focuses on adding edges to improve an existing graph. A major open problem in this field is: Given a graph embedded in a metric space, and a budget of k edges, which k edges do we add to produce a minimum-dilation graph? The special case where k=1 has been studied in the past, but no major breakthroughs have been made for k > 1. We provide the first positive result, an O(k)-approximation algorithm that runs in O(n3 log n) time. © 2022 Copyright held by the owner/author(s). Publication rights licensed to ACM.

关键词： approximation algorithms

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