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Theoretical analysis of GOMP based on RIP and ROC

JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS 2024年第2期41卷 1277-1292页

作者： Li, Haifeng Guo, Leiyan Henan Normal Univ Coll Math & Informat Sci Henan Engn Lab Big Data Stat Anal & Optimal Contro Xinxiang 453007 Peoples R China

This paper aims to investigate sufficient conditions for the recovery of sparse signals via the generalized orthogonal matching pursuit (gOMP) algorithm. In the noisy case, a sufficient condition for recovering the support of k-sparse signal is presented based on restricted isometry property (RIP) and restricted orthogonality constant (ROC).

关键词： Compressed sensing greedy algorithm Restricted isometry property Restricted orthogonality constant

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greedy Sensor Selection for Weighted Linear Least Squares Estimation Under Correlated Noise

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IEEE ACCESS 2022年 10卷 79356-79364页

作者： Yamada, Keigo Saito, Yuji Nonomura, Taku Asai, Keisuke Tohoku Univ Dept Aerosp Engn Sendai Miyagi 9800845 Japan

Optimization of sensor selection has been studied to monitor complex and large-scale systems with data-driven linear reduced-order modeling. An algorithm for greedy sensor selection is presented under the assumption of correlated noise in the sensor signals. A noise model is given using truncated modes in reduced-order modeling, and sensor positions that are optimal for generalized least squares estimation are selected. The determinant of the covariance matrix of the estimation error is minimized by efficient one-rank computations in both underdetermined and overdetermined problems. The present study also reveals that the objective function with correlated noise is neither submodular nor supermodular. Several numerical experiments are conducted using randomly generated data and real-world data. The results show the effectiveness of the selection algorithm in terms of accuracy in the estimation of the states of large-dimensional measurement data.

关键词： Noise measurement Estimation Optimization Mathematical models Covariance matrices greedy algorithms Computational modeling greedy algorithm optimization sensor selection correlated measurement noise

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Nondominated-Solution-Based Multi-Objective greedy Sensor Selection for Optimal Design of Experiments

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2022年 70卷 5694-5707页

作者： Nakai, Kumi Sasaki, Yasuo Nagata, Takayuki Yamada, Keigo Saito, Yuji Nonomura, Taku Natl Inst Adv Ind Sci & Technol Tsukuba 3058564 Japan Tohoku Univ Sendai 9808579 Japan Tohoku Univ Japan Soc Promot Sci Sendai 9808579 Japan Tohoku Univ Dept Aerosp Engn Sendai 9808579 Japan

In this study, a nondominated-solution-based multi-objective greedy method is proposed and applied to a sensor selection problem based on the multiple indices of the optimal design of experiments. The proposed method simultaneously considers multiple set functions and applies the idea of Pareto ranking for the selection of sets. Specifically, a new index is iteratively added to the nondominated solutions of sets, and the multi-objective functions are evaluated for new sets. The nondominated solutions are selected from the examined solutions, and the next sets are then considered. With this procedure, the multi-objective optimization of multiple set functions can be conducted with reasonable computational costs. This paper defines a new class of greedy algorithms which includes the proposed nondominated-solution-based multi-objective greedy algorithm and the group greedy algorithm, and the characteristics of those algorithms are theoretically discussed. Then, the proposed method is applied to the sensor selection problem and its performance is evaluated. The results of the test case show that the proposed method not only gives the Pareto-optimal front of the multi-objective optimization problem but also produces sets of sensors in terms of D-, A-, and E-optimality, that are superior to the sets selected by pure greedy methods that consider only a single objective function.

关键词： Indexes Optimization Linear programming Signal processing algorithms greedy algorithms Search problems Relaxation methods greedy algorithm multi-objective optimization nondominated solution pareto front optimal experimental design data-driven sensor selection

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Non-submodular maximization with a decomposable objective function

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JOURNAL OF COMBINATORIAL OPTIMIZATION 2024年第5期48卷 1-20页

作者： Lu, Cheng Yang, Wenguo Univ Chinese Acad Sci Sch Math Sci Beijing Peoples R China

We study the non-submodular maximization problem, whose objective function can be expressed as the Difference between two Set (DS) functions or the Ratio between two Set (RS) functions. For the cardinality-constrained and unconstrained DS maximization problems, we present several deterministic algorithms and our analysis shows that the algorithms can provide provable approximation guarantees. As an application, we manage to derive an improved approximation bound for the DS minimization problem under certain conditions compared with existing results. As for the RS maximization problem, we show that there exists a polynomial-time reduction from the approximation of RS maximization to the approximation of DS maximization. Based on this reduction, we derive the first approximation bound for the cardinality-constrained RS maximization problem. We also devise algorithms for the unconstrained problem and analyze their approximation guarantees. By applying our results to the problem of optimizing the ratio between two supermodular functions, we give an answer to the question posed by Bai et al. (in Proceedings of The 33rd international conference on machine learning (ICML), 2016). Moreover, we give an example to illustrate that whether the set function is normalized has an effect on the approximability of the RS optimization problem.

关键词： Non-submodular optimization Difference of set functions Ratio of set functions greedy algorithm

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Multiple-Allocation Hub-and-Spoke Network Design With Maximizing Airline Profit Utility in Air Transportation Network

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IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS 2024年第7期25卷 7294-7310页

作者： Yu, Nan Dong, Bin Qu, Yuben Zhang, Mingwei Chen, Guihai Tan, Qingqing Wang, Yanyan Dai, Haipeng State Key Lab Air Traff Management Syst Nanjing 210022 Peoples R China Nanjing Univ Aeronaut & Astronaut Key Lab Dynam Cognit Syst Electromagnet Spectrum S Minist Ind & Informat Technol Nanjing 211106 Peoples R China Nanjing Univ Aeronaut & Astronaut Coll Elect & Informat Engn Nanjing 211106 Peoples R China Nanjing Univ State Key Lab Novel Software Technol Nanjing 210023 Peoples R China Hohai Univ Coll Comp & Informat Nanjing 211100 Peoples R China

Airlines commonly need to take into consideration maximizing their profit while designing the hub-and-spoke network to obtain more market share and promote healthy development of aviation industry. Hence, in this article, we study the problem of multiple-allocation HUb and spoke network design for ROuting flight flows to maximize airline profit utility (HURO). That is, given a set of airport nodes, a set of flight flows with known origin positions and destination positions, finding a limited number of hub edges to transfer flows and determining routing allocation mode considering customer preference such that the overall transportation profit utility is maximized. To address HURO problem, we first consider a relaxed version of HURO (HURO-R for short). We prove that HURO-R falls into the realm of maximizing a submodular set function subject to a cardinality constraint, and propose an algorithm with a constant approximation ratio. Next, we design a two-level algorithm framework with a constant approximation ratio to address HURO. Besides, we consider variants of HURO, HURO-C and HURO-RU, and design approximation algorithms to address them. We conduct simulation experiments on standard dataset and field experiments to verify our theoretical findings. The results shows that our proposed algorithm can outperform other comparison algorithms by 75.28 percent.

关键词： Airline industry Transportation Routing Costs Approximation algorithms Resource management Airports Airline profit cardinality transportation profit utility hub location problem approximation algorithm submodular set function greedy algorithm customer preference routing allocation mode

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Two-stage submodular maximization problem beyond nonnegative and monotone

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MATHEMATICAL STRUCTURES IN COMPUTER SCIENCE 2024年第3期34卷 211-226页

作者： Liu, Zhicheng Chang, Hong Ma, Ran Du, Donglei Zhang, Xiaoyan Nanjing Normal Univ Coll Taizhou Taizhou 225300 Peoples R China Nanjing Normal Univ Sch Math Sci Inst Math Nanjing 210023 Peoples R China Qingdao Univ Technol Sch Management Engn Qingdao 266520 Peoples R China Univ New Brunswick Fac Management Fredericton NB E3B 5A3 Canada

We consider a two-stage submodular maximization problem subject to a cardinality constraint and k matroid constraints, where the objective function is the expected difference of a nonnegative monotone submodular function and a nonnegative monotone modular function. We give two bi-factor approximation algorithms for this problem. The first is a deterministic (1/k+1 (1 - 1/e(k+1)), 1)-approximation algorithm, and the second is a randomized (1/k+1 (1 - 1/e(k+1)), - epsilon, 1)-approximation algorithm with improved time efficiency.

关键词： Submodular maximization greedy algorithm matroid

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On a family of universal cycles for multi-dimensional permutations

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DISCRETE APPLIED MATHEMATICS 2024年 359卷 310-320页

作者： Kitaev, Sergey Qiu, Dun Univ Strathclyde Dept Math & Stat 26 Richmond St Glasgow G1 1XH Scotland Nankai Univ Ctr Combinator LPMC Tianjin 300071 Peoples R China

A universal cycle (u-cycle) for permutations of length n is a cyclic word, any size n window of which is order-isomorphic to exactly one permutation of length n, and all permutations of length n are covered. It is known that u-cycles for permutations exist, and they have been considered in the literature in several papers from different points of view. In this paper, we show how to construct a family of u-cycles for multi-dimensional permutations, which is based on applying an appropriate greedy algorithm. Our construction is a generalization of the greedy way by Gao et al. to construct u-cycles for permutations. We also note the existence of u-cycles for d-dimensional matrices. (c) 2024 Published by Elsevier B.V.

关键词： Universal cycle Combinatorial generation greedy algorithm Multi-dimensional permutation Multi-dimensional matrix

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An Innovative K-Anonymity Privacy-Preserving algorithm to Improve Data Availability in the Context of Big Data

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Computers, Materials & Continua 2024年第4期79卷 1561-1579页

作者： Linlin Yuan Tiantian Zhang Yuling Chen Yuxiang Yang Huang Li State Key Laboratory of Public Big Data College of Computer Science and TechnologyGuizhou UniversityGuiyang550025China College of Information Engineering Guizhou Open UniversityGuiyang550025China Guizhou Academy of Tobacco Science Guiyang550025China

The development of technologies such as big data and blockchain has brought convenience to life,but at the same time,privacy and security issues are becoming more and more *** K-anonymity algorithm is an effective and low computational complexity privacy-preserving algorithm that can safeguard users’privacy by anonymizing big ***,the algorithm currently suffers from the problem of focusing only on improving user privacy while ignoring data *** addition,ignoring the impact of quasi-identified attributes on sensitive attributes causes the usability of the processed data on statistical analysis to be *** on this,we propose a new K-anonymity algorithm to solve the privacy security problem in the context of big data,while guaranteeing improved data ***,we construct a new information loss function based on the information quantity *** that different quasi-identification attributes have different impacts on sensitive attributes,we set weights for each quasi-identification attribute when designing the information loss *** addition,to reduce information loss,we improve K-anonymity in two ***,we make the loss of information smaller than in the original table while guaranteeing privacy based on common artificial intelligence algorithms,i.e.,greedy algorithm and 2-means clustering *** addition,we improve the 2-means clustering algorithm by designing a mean-center method to select the initial center of ***,we design the K-anonymity algorithm of this scheme based on the constructed information loss function,the improved 2-means clustering algorithm,and the greedy algorithm,which reduces the information ***,we experimentally demonstrate the effectiveness of the algorithm in improving the effect of 2-means clustering and reducing information loss.

关键词： Blockchain big data K-anonymity 2-means clustering greedy algorithm mean-center method

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An optimization investigation of enhanced practicality for the OFH/PC scheme based PON monitoring system

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OPTICAL FIBER TECHNOLOGY 2024年 85卷

作者： Deng, Jianfeng Zhang, Xuan Sichuan Normal Univ Coll Phys & Elect Engn Chengdu 610101 Sichuan Peoples R China

We propose a discrete and average approach, focusing on the code set rather than individual codes, for the PON monitoring system based on the optical frequency hopping/periodic code scheme. The discrete and averaged codes are designed to support large-capacity network monitoring, particular for next-generation PONs, while preserving the original encoder structure of the PON monitoring system. The proposed approach discretizes and averages optical frequency hopping/periodic codes with small and large intervals, employing a modified greedy algorithm that mitigates falling into local optimality and an efficient backtracking algorithm, respectively. Our proposed algorithms demonstrate exceptional efficiency and performance, as exemplified by the modified greedy algorithm, which surpasses the exhaustive method by over 2 millionfold in terms of speed. This approach significantly reduces the more rigorously defined probability of multiple-customer interference and lowers the final recognition difficulty, enhancing the practicality of the PON monitoring system. Additionally, we develop a cost-effective model to analyze optimal system costs for discrete-averaged codes in the cost-sensitive PON market, facilitating the practical application of the PON monitoring system in engineering practice.

关键词： Backtracking algorithm greedy algorithm multiple -customers interference probability (MCIP) Network monitoring passive optical network (PON)

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Reduced Basis modelling of turbulence with well-developed inertial range

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COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 2024年 419卷

作者： Moreno, Alejandro Bandera Garcia, Cristina Caravaca Rebollo, Tomas Chacon Avila, Enrique Delgado Marmol, Macarena Gomez Univ Seville IMUS Apdo Correos 1160 Seville 41080 Spain Univ Seville Dept Ecuac Diferenciales & Anal Numer Apdo Correos 1160 Seville 41080 Spain

In this work, we introduce a Reduced Basis model for turbulence at statistical equilibrium. This is based upon an a-posteriori error estimation procedure that measures the distance from a trial solution to the K41 theory energy spectrum. We apply this general idea to build a Reduced Basis Smagorinsky turbulence model through a greedy algorithm. We derive some error estimates that make apparent the role of the energy spectrum in the ROM approximation. We carry on some tests for some academic unsteady 2D flows at large Reynolds number, that present well developed inertial spectrum. The methods presents a high efficiency, as the error achieved with the reduced method is 3 to 4 times the ones achieved if the exact error is used in the greedy algorithm.

关键词： Reduced Order Modelling Large Eddy Simulation Kolmogorov energy cascade Reduced Basis method greedy algorithm

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