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Joint Task Offloading and Service Placement for Mobile Edge Computing: An Online Two-Timescale Approach

IEEE TRANSACTIONS ON CLOUD COMPUTING 2023年第4期11卷 3656-3671页

作者： Li, Xin Zhang, Xinglin Huang, Tiansheng South China Univ Technol Sch Comp Sci & Engn Guangzhou 510006 Guangdong Peoples R China

As a new computing paradigm, mobile edge computing (MEC) pushes the centralized cloud resources close to the edge network, which significantly reduces the pressure of the backbone network and meets the requirements of emerging mobile applications. To achieve high performance of the MEC system, it is essential to design efficient task offloading and service placement schemes, which are responsible for offloading tasks to the edge servers while considering the heterogeneity and diversity of computation services. Our MEC system aims to maximize the long-term average network utility while maintaining the stability of the edge network. Considering that synchronous manner overlooks the scenarios endowed with asymmetric update frequencies for service placement and task offloading, we propose an online algorithm based on the two-timescale Lyapunov optimization in a stochastic network environment without requiring the future information. By making asynchronous decisions on service placement and task offloading with different control parameters $V$V, we can achieve a time-average sub-optimal solution that is close to the offline optimum. In addition, we introduce the varying control parameter $V(t)$V(t) and $\Omega$omega-additive approximation to enhance the robustness of the proposed algorithm within an error Omega. Finally, rigorous theoretical analysis and extensive trace-driven experimental results show that the proposed algorithm achieves the [O(1/V),O(V)] performance-backlog tradeoff and is more competitive than benchmarks.

关键词： Task analysis Cloud computing Costs approximation algorithms Heuristic algorithms Stochastic processes Servers Mobile edge computing service placement task offloading two-timescale lyapunov optimization

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Quartic Riemannian Adaptive Regularization With Cubics for Radar Waveform Design

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IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS 2023年第6期59卷 7514-7528页

作者： Qiu, Xiangfeng Zhang, Xinyu Huo, Kai Jiang, Weidong Natl Univ Def Technol Coll Elect Sci & Technol Changsha 410073 Peoples R China

The ambiguity function is a useful tool for assessing the response performance of radar waveforms. This article addresses the problem of shaping the radar ambiguity function by designing the unimodular transmit waveform. We model the waveform design process as a nonconvex quartic optimization problem aimed at minimizing the disturbance power of scatters in specific range-Doppler bins. Rather than using conventional methods such as approximating and relaxing the objective function and constraints, we address the resultant optimization problem under the Riemannian manifold optimization framework and introduce a novel gradient-based algorithm called quartic Riemannian adaptive regularization with cubics. The developed algorithm applies the Riemannian gradient and Riemannian Hessian of the objective function to conduct iterative operations that gradually decrease the cost function value. The proposed algorithm has a lower iteration complexity bound in comparison to the classical Riemannian trust region method based on the second-order gradient. Numerical experiments demonstrate that our developed method can achieve a relatively higher signal-to-interference ratio with a faster convergence speed.

关键词： Radar Optimization Linear programming Doppler radar Manifolds Doppler effect approximation algorithms Constant modulus constraint cubic regularization Riemannian manifold optimization waveform design

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Online Optimal Event-Triggered H∞ Control for Nonlinear Systems With Constrained State and Input

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IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS 2023年第1期53卷 131-141页

作者： Song, Ruizhuo Liu, Lu Xia, Lina Lewis, Frank L. Univ Sci & Technol Beijing Sch Automat & Elect Engn Beijing Engn Res Ctr Ind Spectrum Imaging Beijing 100083 Peoples R China Univ Texas Arlington UTA Res Inst Ft Worth TX 76012 USA

Taking safety and performance into consideration, the state and control input of the actual engineering system are often constrained. For this kind of problem, this article puts forward an online dual event-triggered (ET) adaptive dynamic programming (ADP) optimal control algorithm for a class of nonlinear systems with constrained state and input. First, the original system is transformed into another system through the barrier function, after that, a suitable value function with a nonquadratic utility function is designed to obtain the optimal control pair. In addition, on the premise of the asymptotic stability of the system, the trigger condition is devised, and the intersampling time analysis is proved that the algorithm can avoid the Zeno phenomenon. What is more, the critic, action, and disturbance neural networks (NNs) are trained to approximate value function and control sequences, subsequently, the approximation error is proved to be uniformly ultimately boundedness (UUB). Finally, two comparative experiments based on the robot arm model are simulated to verify that the algorithm can make control policies update only when the system has the requirement and keep satisfactory control effect, which can effectively decrease the number of data transfers and reduce the calculation burden.

关键词： Optimal control Mathematical models Heuristic algorithms Dynamic programming Asymptotic stability approximation algorithms Safety Adaptive dynamic programming (ADP) constrained system event-triggered (ET) H∞ control

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Performance Analysis and Phase Shift Design of IRS-Aided Uplink OTFS-SCMA

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IEEE ACCESS 2023年 11卷 133059-133069页

作者： Li, Jiarui Hong, Yi Monash Univ Dept Elect & Comp Syst Engn Melbourne Vic 3800 Australia

In this paper, we consider an intelligent reflecting surface (IRS)-aided orthogonal time frequency space (OTFS)-based uplink sparse code multiple access (SCMA) communications system. We first conduct performance analysis in terms of pairwise error probability (PEP) and derive an upper bound on word error probability (WEP). According to this bound, we establish a system design criterion and propose two IRS phase shifts design algorithms using semidefinite relaxation (SDR) and gradient ascent (GA) methods. The computational complexity of these algorithms is discussed. Next, we derive an upper bound on the average bit error rate (BER) and investigate the system performance in terms of diversity and signal-to-noise (SNR) gains. Further, to recover transmitted information bits, we present a modified joint iterative Gaussian approximated message passing (MP) detection and SCMA decoding algorithm, enabling detection and SCMA demapping to occur in each iteration. Finally, simulation results demonstrate that our proposed IRS design algorithms achieve better error performance compared to the known approaches.

关键词： Manganese Uplink Delays approximation algorithms Time-frequency analysis Symbols Performance analysis Intelligent systems Phase shifters Intelligent reflecting surface (IRS) orthogonal time frequency space (OTFS) sparse code multiple access (SCMA) word error probability phase shifts design

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Scheduling on a graph with release times

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JOURNAL OF SCHEDULING 2023年第6期26卷 571-580页

作者： Yu, Wei Golin, Mordecai Zhang, Guochuan East China Univ Sci & Technol Dept Math Shanghai 200237 Peoples R China Hong Kong Univ Sci & Technol Dept Comp Sci & Engn Kowloon Clear Water Bay Hong Kong Peoples R China Zhejiang Univ Coll Comp Sci Hangzhou 310027 Peoples R China

We study a generalization of the well-known traveling salesman problem in a metric space, in which each city is associated with a release time. The salesman has to visit each city at or after its release time. There exists a naive 5/2-approximation algorithm where the salesman simply starts to route the network after all cities are released. Interestingly, this bound has never been improved for more than two decades. In this paper, we revisit the problem and achieve the following results. First, we devise an approximation algorithm with performance ratio less than 5/2 when the number of distinct release times is fixed. Then, we analyze a natural class of algorithms and show that no performance ratio better than 5/2 is possible unless the Metric TSP can be approximated with a ratio strictly less than 3/2, which is a well-known longstanding open question. Finally, we consider a special case where the graph has a heavy edge and present an approximation algorithm with performance ratio less than 5/2.

关键词： Vehicle scheduling problem Traveling salesman problem approximation algorithms Performance ratio

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Robust Interferometric ISAR Imaging With UAMP-Based Joint Sparse Signal Recovery

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IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS 2023年第4期59卷 3890-3906页

作者： Kang, Hailong Li, Jun Guo, Qinghua Martorella, Marco Giusti, Elisa Cai, Jinjian Xidian Univ Hangzhou Inst Technol Hangzhou 311200 Peoples R China Xidian Univ Natl Lab Radar Signal Proc Xian 710071 Peoples R China Univ Wollongong Sch Elect Comp & Telecommun Engn Wollongong NSW 2522 Australia Natl Lab Radar & Surveillance Syst RaSS CNIT Pisa Italy Beijing Inst Technol Key Lab Elect & Informat Technol Satellite Nav Minist Educ Beijing 100081 Peoples R China Natl Lab Radar & Surveillance Syst CNIT I-56124 Pisa Italy

Sparse Bayesian learning (SBL) has found successful applications in interferometric inverse synthetic aperture radar (InISAR) imaging, especially in the presence of limited number of pulses or when using sparse apertures. SBL-based InISAR algorithms have been proven to be significantly superior to Fourier transform-based ones. However, the existing SBL-based algorithms are slow due to their high computational complexity. Moreover, there is also much room to improve in terms of imaging performance. In this article, leveraging the approximate message passing with unitary transformation (UAMP), we propose an InISAR imaging algorithm named UAMP joint sparse recovery (JSR), which is much faster and delivers notably higher imaging accuracy than the existing SBL-based algorithms. Specifically, we develop a type-2 joint sparse model for InISAR imaging and formulate it as a two-layer multiple measurement vectors joint sparse problem. Based on a factor graph representation, the message passing techniques are used to efficiently solve this problem, which leads to the UAMP-JSR algorithm. Results based on extensive simulations and experiments based on the real data collected by the Pisa Radar demonstrate the effectiveness and superiority of the proposed algorithm compared to existing algorithms.

关键词： Imaging Radar imaging approximation algorithms Three-dimensional displays Signal processing algorithms Antenna measurements Spaceborne radar Interferometric inverse synthetic aperture radar (InISAR) joint sparse recovery sparse Bayesian learning (SBL) unitary transformation (UAMP)

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Unsplittable Euclidean Capacitated Vehicle Routing: A (2 + ϵ)-approximation Algorithm 14

Unsplittable Euclidean Capacitated Vehicle Routing: A (2 + ...

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14th Innovations in Theoretical Computer Science Conference, ITCS 2023

作者： Grandoni, Fabrizio Mathieu, Claire Zhou, Hang IDSIA USI-SUPSI Lugano Switzerland CNRS IRIF Université de Paris France École Polytechnique Institut Polytechnique de Paris France

ISBN: (纸本)9783959772631

In the unsplittable capacitated vehicle routing problem, we are given a metric space with a vertex called depot and a set of vertices called terminals. Each terminal is associated with a positive demand between 0 and 1. The goal is to find a minimum length collection of tours starting and ending at the depot such that the demand of each terminal is covered by a single tour (i.e., the demand cannot be split), and the total demand of the terminals in each tour does not exceed the capacity of 1. Our main result is a polynomial-time (2 + ϵ)-approximation algorithm for this problem in the two-dimensional Euclidean plane, i.e., for the special case where the terminals and the depot are associated with points in the Euclidean plane and their distances are defined accordingly. This improves on recent work by Blauth, Traub, and Vygen [IPCO'21] and Friggstad, Mousavi, Rahgoshay, and Salavatipour [IPCO'22]. © Fabrizio Grandoni, Claire Mathieu, and Hang Zhou;licensed under Creative Commons License CC-BY 4.0.

关键词： approximation algorithms

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Round and Bipartize for Vertex Cover approximation 26

Round and Bipartize for Vertex Cover Approximation

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26th International Conference on approximation algorithms for Combinatorial Optimization Problems, APPROX 2023 and the 27th International Conference on Randomization and Computation, RANDOM 2023

作者： Kashaev, Danish Schäfer, Guido Centrum Wiskunde & Informatica Amsterdam Netherlands ILLC University of Amsterdam Netherlands

ISBN: (纸本)9783959772969

The vertex cover problem is a fundamental and widely studied combinatorial optimization problem. It is known that its standard linear programming relaxation is integral for bipartite graphs and half-integral for general graphs. As a consequence, the natural rounding algorithm based on this relaxation computes an optimal solution for bipartite graphs and a 2-approximation for general graphs. This raises the question of whether one can interpolate the rounding curve of the standard linear programming relaxation in a beyond the worst-case manner, depending on how close the graph is to being bipartite. In this paper, we consider a round-and-bipartize algorithm that exploits the knowledge of an induced bipartite subgraph to attain improved approximation ratios. Equivalently, we suppose that we work with a pair (G, S), consisting of a graph with an odd cycle transversal. If S is a stable set, we prove a tight approximation ratio of 1 + 1/ρ, where 2ρ − 1 denotes the odd girth (i.e., length of the shortest odd cycle) of the contracted graph G˜:= G/S and satisfies ρ ∈ [2, ∞], with ρ = ∞ corresponding to the bipartite case. If S is an arbitrary set, we prove a tight approximation ratio of (1 + 1/ρ) (1 − α) + 2α, where α ∈ [0, 1] is a natural parameter measuring the quality of the set S. The technique used to prove tight improved approximation ratios relies on a structural analysis of the contracted graph G˜, in combination with an understanding of the weight space where the fully half-integral solution is optimal. Tightness is shown by constructing classes of weight functions matching the obtained upper bounds. As a byproduct of the structural analysis, we also obtain improved tight bounds on the integrality gap and the fractional chromatic number of 3-colorable graphs. We also discuss algorithmic applications in order to find good odd cycle transversals, connecting to the MinUncut and Colouring problems. Finally, we show that our analysis is optimal in the following sense: t

关键词： approximation algorithms

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Polynomial-Time approximation of Independent Set Parameterized by Treewidth 31

Polynomial-Time Approximation of Independent Set Parameteriz...

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31st Annual European Symposium on algorithms, ESA 2023

作者： Chalermsook, Parinya Fomin, Fedor Hamm, Thekla Korhonen, Tuukka Nederlof, Jesper Orgo, Ly Aalto University Finland University of Bergen Norway Utrecht University Netherlands

ISBN: (纸本)9783959772952

We prove the following result about approximating the maximum independent set in a graph. Informally, we show that any approximation algorithm with a "non-trivial" approximation ratio (as a function of the number of vertices of the input graph G) can be turned into an approximation algorithm achieving almost the same ratio, albeit as a function of the treewidth of G. More formally, we prove that for any function f, the existence of a polynomial time (n/f(n))-approximation algorithm yields the existence of a polynomial time O(tw · log f(tw)/f(tw))-approximation algorithm, where n and tw denote the number of vertices and the width of a given tree decomposition of the input graph. By pipelining our result with the state-of-the-art O(n · (log log n)2 / log3 n)-approximation algorithm by Feige (2004), this implies an O(tw · (log log tw)3 / log3 tw)-approximation algorithm. © Parinya Chalermsook, Fedor Fomin, Thekla Hamm, Tuukka Korhonen, Jesper Nederlof, and Ly Orgo.

关键词： approximation algorithms

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An approximation Algorithm for Distance-Constrained Vehicle Routing on Trees 40

An Approximation Algorithm for Distance-Constrained Vehicle ...

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40th International Symposium on Theoretical Aspects of Computer Science, STACS 2023

作者： Dufay, Marc Mathieu, Claire Zhou, Hang École Polytechnique IRIF Palaiseau France CNRS Paris France École Polytechnique Palaiseau France

ISBN: (纸本)9783959772662

In the Distance-constrained Vehicle Routing Problem (DVRP), we are given a graph with integer edge weights, a depot, a set of n terminals, and a distance constraint D. The goal is to find a minimum number of tours starting and ending at the depot such that those tours together cover all the terminals and the length of each tour is at most D. The DVRP on trees is of independent interest, because it is equivalent to the "virtual machine packing" problem on trees studied by Sindelar et al. [SPAA’11]. We design a simple and natural approximation algorithm for the tree DVRP, parameterized by Ε > 0. We show that its approximation ratio is α + Ε, where α ≈ 1.691, and in addition, that our analysis is essentially tight. The running time is polynomial in n and D. The approximation ratio improves on the ratio of 2 due to Nagarajan and Ravi [Networks’12]. The main novelty of this paper lies in the analysis of the algorithm. It relies on a reduction from the tree DVRP to the bounded space online bin packing problem via a new notion of "reduced length". © Marc Dufay, Claire Mathieu, and Hang Zhou.

关键词： approximation algorithms

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