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Two-Round Optimization Algorithm Based on Quadric Error Metrics

IEEE ACCESS 2025年 13卷 30021-30035页

作者： Chang, Han Zhang, Di Dong, Yanan Yang, Yijun Shafiq Ur Rehman Khalil, Hafiz Wang, Xueting Xi An Jiao Tong Univ Sch Human Settlement & Civil Engn Dept Architecture Xian 710049 Peoples R China Xi An Jiao Tong Univ Sch Comp Sci & Technol Xian 710049 Peoples R China

Triangular mesh models are widely used for 3D model displays, but large models can cause slow loading and transmission, especially on mobile or web platforms. The quadric error metrics (QEM) algorithm is known for its efficient simplification and effectiveness. Nevertheless, it lacks clear prioritization for folding flat areas within the model, leaving room for improvement. This paper reproduces the work of Zhang Yun et al., finding that while their method reduces simplification errors, it increases the folding time of flat areas. The study improves the QEM algorithm by combining the angle and area of the first-order neighboring triangles of the edge, resulting in faster simplification but higher errors, making it less versatile. To address these issues, a two-round simplification method is proposed. The first round simplifies planar areas, and the second focuses on the entire model. Compared to the recursive algorithm, the two-round method showcases shorter simplification times, particularly evident when the *** exhibits a lower simplification ratio. For simplification rates below 40%, it reduces the average simplification time by 22.77% and yields better model accuracy than the QEM algorithm. On bunny_***, the simplification error is smaller than with the QEM algorithm, showcasing an average error reduction of 21.82%. Visually, the two-round proposed algorithm retains more detailed features and has better visual effects. However, because of the lower computational efficiency of the two-round simplification, future research directions may involve parallel computing and GPU utilization for acceleration.

关键词： approximation algorithms Solid modeling Three-dimensional displays Vectors Measurement uncertainty Costs Faces Load modeling Computational modeling Clustering algorithms Quadric error metrics two-round proposed algorithm first-order neighborhood triangle area approximate curvature

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Multiplatform Bearing-Only Target Tracking Algorithm Based on Maximum Likelihood Maximum Correntropy Kalman Filter

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IEEE SENSORS JOURNAL 2025年第7期25卷 11366-11377页

作者： Zhang, Kai Wang, Hongjian Chen, Weihao Ren, Jingfei Luo, Naifu Lu, Zhenwei Harbin Engn Univ Coll Intelligent Syst Sci & Engn Harbin 150001 Peoples R China Wuhan Second Ship Design & Res Inst Wuhan 430205 Peoples R China

Multiplatform bearing-only target tracking poses a significant challenge in underwater target tracking. Presently, the field often relies on suboptimal nonlinear filters, which unfortunately exhibit numerical instability when confronted with highly nonlinear systems. Hence, this article suggests employing the maximum likelihood Kalman filtering (MLKF) algorithm for multiplatform bearing-only target tracking. This approach first obtains the maximum likelihood estimate (MLE) of the bearings from multiple nonlinear measurements, which are then converted into the target's position in Cartesian coordinates for the Kalman filter (KF). The KF algorithm is derived based on the assumption of Gaussian noise. However, in engineering practice, measurement noise is often non-Gaussian, which can lead to a decline in the tracking accuracy of the KF algorithm. To address this, the maximum likelihood maximum correntropy KF (MLMCKF) algorithm is proposed, which utilizes the maximum correntropy criterion (MCC) instead of the original minimum mean square error (MMSE) criterion. Simulation results show that the measurement values transformed by the ML method follow a Gaussian distribution. Moreover, under non-Gaussian measurement noise, the proposed MCMLKF algorithm achieves superior tracking accuracy compared to existing non-Gaussian algorithms.

关键词： Target tracking Noise Maximum likelihood estimation Noise measurement Kalman filters Heuristic algorithms approximation algorithms Accuracy Position measurement Chatbots Bearing-only Kalman filter (KF) maximum correntropy criterion (MCC) maximum likelihood estimate (MLE) target tracking

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Sorting genomes by prefix double-cut-and-joins

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THEORETICAL COMPUTER SCIENCE 2025年 1024卷

作者： Fertin, Guillaume Jean, Geraldine Labarre, Anthony Nantes Univ Ecole Cent Nantes CNRS LS2NUMR 6004 F-44000 Nantes France Univ Gustave Eiffel CNRS Lab Informat Gaspard Monge ENPCESIEE ParisUPEMLIGMUMR 8049 F-77454 Marne la Vallee France

In this paper, we study the problem of sorting unichromosomal linear genomes by prefix double- cut-and-joins (or DCJs) in both the signed and the unsigned settings. Prefix DCJs cut the leftmost segment of a genome and any other segment, and recombine the severed endpoints in one of two possible ways: one of these options corresponds to a prefix reversal, which reverses the order of elements between the two cuts (as well as their signs in the signed case). Our main results are: (1) new structural lower bounds based on the breakpoint graph for sorting by unsigned prefix reversals, unsigned prefix DCJs, and signed prefix DCJs;(2) two polynomial-time algorithms for sorting by prefix DCJs, both in the signed case (which answers an open question of Labarre [1]) and in the unsigned case;(3) a 1-absolute approximation algorithm for sorting by unsigned prefix reversals for a specific class of permutations.

关键词： Genome rearrangements Prefix reversals Prefix DCJs Lower bounds Algorithmics approximation algorithms

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Adaptive Digital Twin Migration in Vehicular Edge Computing and Networks

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IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY 2025年第3期74卷 4839-4854页

作者： Mou, Fangyi Lou, Jiong Tang, Zhiqing Wu, Yuan Jia, Weijia Zhang, Yan Zhao, Wei Hong Kong Baptist Univ Kowloon Tong Hong Kong Peoples R China Shanghai Jiao Tong Univ Dept Comp Sci & Engn Shanghai 200240 Peoples R China Beijing Normal Univ Inst Artificial Intelligence & Future Networks Zhuhai 519087 Peoples R China Univ Macau State Key Lab IoT Smart City Macau 999078 Peoples R China BNU HKBU United Int Coll Guangdong Key Lab AI & Multimodal Data Proc Zhuhai 519087 Peoples R China Univ Oslo Dept Informat N-0316 Oslo Norway Shenzhen Univ Adv Technol Shenzhen 518055 Peoples R China

The surge in mobile vehicles and data traffic in Vehicular Edge Computing and Networks (VECONs) requires innovative approaches for low latency, stable connectivity, and efficient resource usage in fast-moving vehicles. Existing studies have identified that utilizing digital twins (DTs) can effectively improve service quality in VECONs. However, it still faces substantial challenges posed by large-scale complex DT communications in sustaining real-time collaborative endeavors. In particular, within the dynamic VECONs, the decision regarding DT migration plays a pivotal role in sustaining the quality of services. In this paper, we propose an adaptive DT migration (ADM) algorithm to minimize the overall migration costs when DTs deliver services. Specifically, 1) We formulate ADM as a combinatorial optimization problem in VECONs, comprehensively considering communication latency and migration latency under complex DT communications, vehicular mobilities, and dynamic states of edges;2) An ADM algorithm based on off-policy actor-critic reinforcement learning is proposed to make migration decisions. Moreover, the ADM agent employs warm-up policies to address exploration challenges in sparse state spaces;3) Simulations based on real-world, large-scale urban vehicular mobility datasets demonstrate that our method outperforms existing algorithms by approximately 39% on average, and it can achieve results close to the optimal.

关键词： Vehicle dynamics Real-time systems Heuristic algorithms Costs Feature extraction Edge computing approximation algorithms Adaptive systems Servers Training Digital twin migration vehicular edge computing deep reinforcement learning

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Submodular Order Functions and Assortment Optimization

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MANAGEMENT SCIENCE 2025年第1期71卷 202-218页

作者： Udwani, Rajan Univ Calif Berkeley Ind Engn & Operat Res Berkeley CA 94720 USA

We define a new class of set functions that, in addition to being monotone and subadditive, also admit a very limited form of submodularity defined over a permutation of the ground set. We refer to this permutation as a submodular order. This class of functions includes monotone submodular functions as a subfamily. We give fast algorithms with strong approximation guarantees for maximizing submodular order functions under a variety of constraints and show a nearly tight upper bound on the highest approximation guarantee achievable by algorithms with polynomial query complexity. Applying this new notion to the problem of constrained assortment optimization in fundamental choice models, we obtain new algorithms that are both faster and have stronger approximation guarantees (in some cases, first algorithm with constant factor guarantee). We also show an intriguing connection to the maximization of monotone submodular functions in the streaming model, where we recover best known approximation guarantees as a corollary of our results.

关键词： submodular order assortment optimization approximation algorithms

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An LP-Based approximation Algorithm for the Fault-Tolerant Facility Location Problem with Penalties 25th

An LP-Based Approximation Algorithm for the Fault-Tolerant...

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25th International Conference on Parallel and Distributed Computing, Applications and Technologies, PDCAT 2024

作者： Guo, Yingying Li, Qiaoliang School of Mathematics and Statistics Hunan Normal University Hunan Changsha410081 China

ISBN: (纸本)9789819642069

We consider the fault-tolerant facility location problem with penalties. In this problem, we replicate each client vj times. Some of these replicas are connected to opened facility, while others remain unconnected and are penalized. By employing a natural LP-rounding technique, we provide a 2-approximation algorithm for this problem. In this algorithm, we balance the connection cost and penalty cost by setting thresholds. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2025.

关键词： approximation algorithms

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Gradient-Guided Local Search for Large-Scale Hypervolume Subset Selection

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IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION 2025年第2期29卷 519-533页

作者： Nan, Yang Shu, Tianye Ishibuchi, Hisao Shang, Ke Southern Univ Sci & Technol Dept Comp Sci & Engn Shenzhen 518055 Peoples R China Shenzhen Univ Natl Engn Lab Big Data Syst Comp Technol Shenzhen 518060 Peoples R China

The use of an unbounded archive (UA) has attracted much attention in the filed of evolutionary multiobjective optimization (EMO) since a solution set selected from the UA is often better than the final population. The size of the UA is very large (e.g., 1 000 000) since it is unbounded and it stores all the examined nondominated solutions during the execution of an EMO algorithm. Thus, an algorithm which can efficiently select a high-quality subset from a large-scale candidate set (e.g., UA) is needed. In this article, we propose a gradient-guided local search hypervolume subset selection (GL-HSS) algorithm to efficiently select a high-quality subset from a large-scale candidate set. In each iteration of GL-HSS, the gradient of the hypervolume (HV) contribution of each selected solution is used to guide the local search. As a result, the proposed algorithm can quickly improve the HV of the selected subset. Experimental results show that, compared to the existing subset selection algorithms, the proposed GL-HSS algorithm can efficiently select high-quality subsets from various large-scale candidate sets.

关键词： approximation algorithms Classification algorithms Search problems Optimization Vectors Evolutionary computation Minimization Time complexity Size measurement Indexes Evolutionary multiobjective optimization (EMO) hypervolume subset selection (HSS) local search (LS) many-objective optimization

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Efficient Computation of Collatz Sequence Stopping Times: A Novel Algorithmic Approach

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IEEE ACCESS 2025年 13卷 41210-41220页

作者： Getachew, Eyob Solomon Assefa, Beakal Gizachew Addis Ababa Inst Technol Sch Informat Technol & Engn Addis Ababa 1000 Ethiopia

The Collatz conjecture, which posits that any positive integer will eventually reach 1 through a specific iterative process, is a classic unsolved problem in mathematics. This research focuses on designing an efficient algorithm to compute the stopping time of numbers in the Collatz sequence, achieving significant computational improvements. By leveraging structural patterns in the Collatz tree, the proposed algorithm minimizes redundant operations and optimizes computational steps. Unlike prior methods, it efficiently handles extremely large numbers without requiring advanced techniques such as memoization or parallelization. Experimental evaluations confirm computational efficiency improvements of approximately 28% over state-of-the-art methods. These findings underscore the algorithm's scalability and robustness, providing a foundation for future large-scale verification of the conjecture and potential applications in computational mathematics.

关键词： Computational efficiency Encryption approximation algorithms Visualization Probabilistic logic Optimization Complexity theory Watermarking Time complexity Testing Algorithm optimization bitwise operations Collatz conjecture Collatz tree computational mathematics high-performance algorithms logarithmic complexity memoization parallel computing stopping time computational complexity sequence analysis and large-scale verification

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Data-Efficient Off-Policy Learning for Distributed Optimal Tracking Control of HMAS With Unidentified Exosystem Dynamics

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IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2024年第3期35卷 3181-3190页

作者： Xu, Yong Wu, Zheng-Guang Beijing Inst Technol Sch Automat Beijing 100081 Peoples R China Zhejiang Univ Inst Cyber Syst & Control Hangzhou 310027 Peoples R China

In this article, a data-efficient off-policy reinforcement learning (RL) approach is proposed for distributed output tracking control of heterogeneous multiagent systems (HMASs) using approximate dynamic programming (ADP). Different from existing results that the kinematic model of the exosystem is addressable to partial or all agents, the dynamics of the exosystem are assumed to be completely unknown for all agents in this article. To solve this difficulty, an identifiable algorithm using the experience-replay method is designed for each agent to identify the system matrices of the novel reference model instead of the original exosystem. Then, an output-based distributed adaptive output observer is proposed to provide the estimations of the leader, and the proposed observer not only has a low dimension and less data transmission among agents but also is implemented in a fully distributed way. Besides, a data-efficient RL algorithm is given to design the optimal controller offline along with the system trajectories without solving output regulator equations. An ADP approach is developed to iteratively solve game algebraic Riccati equations (GAREs) using online information of state and input in an online way, which relaxes the requirement of knowing prior knowledge of agents' system matrices in an offline way. Finally, a numerical example is provided to verify the effectiveness of theoretical analysis.

关键词： Heuristic algorithms Observers Mathematical models approximation algorithms Multi-agent systems Symmetric matrices Regulation Adaptive observer approximate dynamic programming (ADP) heterogeneous multiagent systems (HMASs) output tracking reinforcement learning (RL)

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Age of Information Diffusion on Social Networks

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IEEE TRANSACTIONS ON NETWORKING 2025年第2期33卷 701-712页

作者： Li, Songhua Duan, Lingjie Singapore Univ Technol & Design Pillar Engn Syst & Design Singapore City 487372 Singapore

To promote viral marketing, major social platforms (e.g., Facebook Marketplace and Pinduoduo) repeatedly select and invite different users (as seeds) in online social networks to share fresh information about a product or service with their friends. Thereby, we are motivated to optimize a multi-stage seeding process of viral marketing in social networks, and adopt the recent notions of the peak and the average age of information (AoI) to measure the timeliness of promotion information received by network users. Our problem is different from the literature on information diffusion in social networks, which limits to one-time seeding and overlooks AoI dynamics or information replacement over time. As a critical step, we manage to develop closed-form expressions that characterize and trace AoI dynamics over any social network. For the peak AoI problem, we first prove the NP-hardness of our multi-stage seeding problem by a highly non-straightforward reduction from the dominating set problem, and then present a new polynomial-time algorithm that achieves good approximation guarantees (e.g., less than 2 for linear network topology). To minimize the average AoI, we also prove that our problem is NP-hard by properly reducing it from the set cover problem. Benefiting from our two-sided bound analysis on the average AoI objective, we build up a new framework for approximation analysis and link our problem to a much simplified sum-distance minimization problem. This intriguing connection inspires us to develop another polynomial-time algorithm that achieves a good approximation guarantee. Additionally, our theoretical results are well corroborated by experiments on a real social network.

关键词： approximation algorithms Minimization Information diffusion Information age Network topology Heuristic algorithms Monitoring Closed-form solutions Topology Receivers Age of information social network multi-stage seeding NP-hardness approximation algorithms

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