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Better approximation for Distributed Weighted Vertex Cover via Game-Theoretic Learning

IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS 2022年第8期52卷 5308-5319页

作者： Sun, Changhao Qiu, Huaxin Sun, Wei Chen, Qian Su, Li Wang, Xiaochu Zhou, Qingrui China Acad Space Technol Qian Xuesen Lab Space Technol Beijing 100094 Peoples R China Xidian Univ Sch Aerosp Sci & Technol Xian 710071 Peoples R China Southeast Univ Sch Automat Nanjing 210096 Peoples R China Capital Normal Univ Sch Informat Engn Beijing 100089 Peoples R China

Toward better approximation for the minimum-weighted vertex cover (MWVC) problem in multiagent systems, we present a distributed algorithm from the perspective of learning in games. For self-organized coordination and optimization, we see each vertex as a potential game player who makes decisions using local information of its own and the immediate neighbors. The resulting Nash equilibrium is classified into two categories, i.e., the inferior Nash equilibrium (INE) and the dominant Nash equilibrium (DNE). We show that the optimal solution must be a DNE. To achieve better approximation ratios, local rules of perturbation and weighted memory are designed, with the former destroying the stability of an INE and the latter facilitating the refinement of a DNE. By showing the existence of an improvement path from any INE to a DNE, we prove that when the memory length is larger than 1, our algorithm converges in finite time to DNEs, which could not be improved by exchanging the action of a selected node with all its unselected neighbors. Moreover, additional freedom for solution efficiency refinement is provided by increasing the memory length. Finally, intensive comparison experiments demonstrate the superiority of the presented methodology to the state of the art, both in solution efficiency and computation speed.

关键词： Games Sun Nash equilibrium Optimization Optimized production technology approximation algorithms Space technology Distributed decision making game-theoretic optimization minimum-weighted vertex cover (MWVC) Nash equilibrium potential game

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k-Median/Means with Outliers Revisited: A Simple Fpt approximation 29th

k-Median/Means with Outliers Revisited: A Simple Fpt Approx...

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29th International Computing and Combinatorics Conference, COCOON 2023

作者： Chen, Xianrun Han, Lu Xu, Dachuan Xu, Yicheng Zhang, Yong Chinese Academy of Sciences Shenzhen Institute of Advanced Technology Shenzhen China Beijing University of Posts and Telecommunications Beijing China Beijing University of Technology Beijing China

ISBN: (纸本)9783031491924

We revisit the classical metric k-median/means with outliers in this paper, whose proposal dates back to (Charikar, Khuller, Mount, and Narasimhan SODA’01). Though good approximation algorithms have been proposed, referring to the state-of-the-art (6.994+ Ε )-approximation (Gupta, Moseley and Zhou ICALP’21) for k-median with outliers and (53.002+ Ε )-approximation (Krishnaswamy, Li, and Sandeep SODA’18) for k-means with outliers respectively, we are interested in finding efficient fpt (fixed-parameter tractable) approximations, following a recent research mainstream for constrained clusterings. As our main contribution, we propose a simple but efficient technical framework that yields a (3 + Ε) / (9 + Ε) -approximation for k-median/means with outliers, albeit in ((m+ k) / Ε) O(k)· nO(1) time. It is notable that our results match with previous result (Goyal, Jaiswal, and Kumar IPEC’20) in terms of ratio and asymptotic running time. But as aforementioned, our technique is much more simplified and straightforward, where instead of considering the whole client set, we restrict ourselves to finding a good approximate facility set for coreset, which can be done easily in fpt time even with provably small loss. Similar idea can be applied to more constrained clustering problems whose coresets have been well-studied. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.

关键词： approximation algorithms

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A constant-factor approximation for directed latency in quasi-polynomial time

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JOURNAL OF COMPUTER AND SYSTEM SCIENCES 2022年 126卷 44-58页

作者： Friggstad, Zachary Swamy, Chaitanya Univ Alberta Dept Comp Sci Edmonton AB Canada Univ Waterloo Dept Combinator & Optimizat Waterloo ON Canada

We consider the directed minimum latency problem (DirLat), wherein we seek a path P visiting all points (or clients) in a given asymmetric metric starting at a given root node r, so as to minimize the sum of the client waiting times along P. We give the first constantfactor approximation guarantee for DirLat, but in quasi-polynomial time. A key ingredient of our result, and our chief technical contribution, is an extension of a recent result of Kohne et al. (2019) [17] showing that the integrality gap of the natural Held-Karp relaxation for asymmetric TSP-Path (ATSPP) is at most a constant. We also give a better approximation guarantee for the minimum total-regret problem, where the goal is to find a path P that minimizes the total time that nodes spend in excess of their shortest-path distances from r, which can be cast as a special case of DirLat involving so-called regret metrics. (c) 2021 Elsevier Inc. All rights reserved.

关键词： approximation algorithms Directed latency Asymmetric TSP LP-rounding

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Internal Model-Based Online Optimization

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2024年第1期69卷 689-696页

作者： Bastianello, Nicola Carli, Ruggero Zampieri, Sandro KTH Royal Inst Technol Sch Elect Engn & Comp Sci S-11428 Stockholm Sweden Univ Padua Dept Informat Engn DEI I-35131 Padua Italy

In this article, we propose a model-based approach to the design of online optimization algorithms, with the goal of improving the tracking of the solution trajectory (trajectories) w.r.t. state-of-the-art methods. We focus first on quadratic problems with a time-varying linear term, and use digital control tools (a robust internal model principle) to propose a novel online algorithm that can achieve zero tracking error by modeling the cost with a dynamical system. We prove the convergence of the algorithm for both strongly convex and convex problems. We further discuss the sensitivity of the proposed method to model uncertainties and quantify its performance. We discuss how the proposed algorithm can be applied to general (nonquadratic) problems using an approximate model of the cost, and analyze the convergence leveraging the small gain theorem. We present numerical results that showcase the superior performance of the proposed algorithms over previous methods for both quadratic and nonquadratic problems.

关键词： Signal processing algorithms Optimization Heuristic algorithms Costs Trajectory Convergence approximation algorithms Digital control online gradient descent online optimization robust control structured algorithms

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A Spiking Reinforcement Trajectory Planning for UAV-Assisted MEC Systems

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IEEE ACCESS 2024年 12卷 54435-54448页

作者： Xia, Zeyang Dong, Li Jiang, Feibo Hunan Univ Technol & Business Sch Comp Sci Changsha 410205 Peoples R China Xiangjiang Lab Changsha 410205 Peoples R China Hunan Normal Univ Coll Informat Sci & Engn Changsha 410081 Peoples R China

This study aims to minimize the energy consumption of user equipments (UE) and unmanned aerial vehicles (UAV) in UAV-assisted mobile edge computing (MEC) systems through the optimization of UAV flight trajectories, user associations, and resource allocations. The problem is formally articulated as a mixed integer nonlinear programming (MINLP) problem. However, employing deep reinforcement learning (DRL) to address this challenge introduces computational complexity and convergence obstacles. In response to these challenges, we propose an efficient and robust approach known as spiking reinforcement trajectory planning (SRTP), which uniquely integrates spiking neural networks (SNN) with DRL. SRTP utilizes a Poisson encoding mechanism to seamlessly convert between spike and continuous signals, enabling collaborative learning between spike actor networks and deep critic networks. Additionally, a pseudo-spacetime backpropagation method is employed for accelerated training of the spike actor network. Experimental findings distinctly highlight SRTP's advantages, demonstrating a more streamlined network structure and faster convergence compared to conventional methodologies. This innovative methodology holds promise in addressing the computational complexities and convergence challenges associated with implementing DRL in UAV-assisted MEC systems.

关键词： Autonomous aerial vehicles Task analysis Training Trajectory Optimization approximation algorithms Trajectory planning Multi-access edge computing Edge computing Mobile edge computing spiking neural network deep reinforcement learning unmanned aerial vehicle trajectory planning

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Efficient algorithms for Service Chaining in NFV-Enabled Satellite Edge Networks

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IEEE TRANSACTIONS ON MOBILE COMPUTING 2024年第5期23卷 5677-5694页

作者： Xia, Qiufen Wang, Guijie Xu, Zichuan Liang, Weifa Xu, Zhou Dalian Univ Technol Int Sch Informat Sci & Engn Dalian 116024 Liaoning Peoples R China Key Lab Ubiquitous Network & Serv Software Liaonin Dalian 116024 Liaoning Peoples R China Dalian Univ Technol Sch Software Dalian 116024 Liaoning Peoples R China City Univ Hong Kong Dept Comp Sci Hong Kong Peoples R China

Satellite-terrestrial networks are emerging as the next-generation networking paradigm for Beyond-5 G (B5G) and 6 G networks. Meanwhile, Mobile Edge Computing (MEC) is envisioned as the key technology to provide network services within the proximity of users, by deploying computing resource in ground locations that are close to users. With the fast deployment of Low-Earth-Oribt (LEO) satellites, a new paradigm of MEC is emerging by enabling LEO satellites serving as edge servers in lower orbits that are close to ground users. In this way, the ground users can be further served by LEO satellites in lower orbits instead of conventional high-orbit satellites. Also, since LEO satellites provide shorter paths from users to services, the performance is enhanced compared with ground MEC networks. In this paper, we aim to enable low-latency network services in a Satellite Edge Computing (SEC) network that integrates the MEC and satellite-terrestrial networks. In particular, we consider that each network service is composed of a sequence of Virtualized Network Functions (VNFs), where the traffic of user requests has to be processed by the VNFs in a service chain in the specified order before reaching its destination. To this end, we first formulate a delay-aware service chaining problem in an SEC network to minimize the average delay of implementing a user request, by jointly placing VNFs to LEO satellites in the SEC network and routing the traffic of each user request from its source to destination. We then devise an approximation algorithm with an approximation ratio for the problem in an SEC network with a single user request, by devising a novel concept of chaining orbit and auxiliary graph construction technique. We also design an online algorithm for the online delay-aware service chaining problem in an SEC network, if user requests arrive into the system without the knowledge of their arrivals and the network delays are uncertain. We finally evaluate the performance o

关键词： Satellites Low earth orbit satellites Delays Orbits Internet of Things approximation algorithms Low latency communication approximation and online algorithms mobile edge computing network function chaining satellite edge network

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Multi-Scale Energy (MuSE) Framework for Inverse Problems in Imaging

IEEE TRANSACTIONS ON COMPUTATIONAL IMAGING

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IEEE TRANSACTIONS ON COMPUTATIONAL IMAGING 2024年 10卷 1250-1265页

作者： Chand, Jyothi Rikhab Jacob, Mathews Univ Iowa Dept Elect & Comp Engn Iowa City IA 52242 USA Univ Virginia Dept Elect & Comp Engn Charlottesville VA 22903 USA

We introduce multi-scale energy models to learn the prior distribution of images, which can be used in inverse problems to derive the Maximum A Posteriori (MAP) estimate and to sample from the posterior distribution. Compared to the traditional single-scale energy models, the multi-scale strategy improves the estimation accuracy and convergence of the MAP algorithm, even when it is initialized far away from the solution. We propose two kinds of multi-scale strategies: a) the explicit (e-MuSE) framework, where we use a sequence of explicit energies, each corresponding to a smooth approximation of the original negative log-prior, and b) the implicit (i-MuSE), where we rely on a single energy function whose gradients at different scales closely match the corresponding e-MuSE gradients. Although both schemes improve convergence and accuracy, the e-MuSE MAP solution depends on the scheduling strategy, including the choice of intermediate scales and exit conditions. In contrast, the i-MuSE formulation is significantly simpler, resulting in faster convergence and improved performance. We compare the performance of the proposed MuSE models in the context of Magnetic Resonance (MR) image recovery. The results demonstrate that the multi-scale framework yields a MAP reconstruction comparable in quality to the End-to-End (E2E) trained models, while being relatively unaffected by the changes in the forward model. In addition, the i-MuSE scheme also allows the generation of samples from the posterior distribution, enabling us to estimate the uncertainty maps.

关键词： Convergence Computational modeling Estimation Diffusion models Imaging approximation algorithms Manifolds Energy model multi-scale Maximum A Posteriori (MAP) estimate sampling uncertainty

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AN IMPROVED approximation ALGORITHM FOR THE ASYMMETRIC TRAVELING SALESMAN PROBLEM\ast

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SIAM JOURNAL ON COMPUTING 2022年第1期51卷 139-173页

作者： Traub, Vera Vygen, Jens Swiss Fed Inst Technol Dept Math CH-8092 Zurich Switzerland Univ Bonn Res Inst Discrete Math D-53113 Bonn Germany Univ Bonn Hausdorff Ctr Math D-53113 Bonn Germany

We revisit the constant-factor approximation algorithm for the asymmetric traveling salesman problem by Svensson, Tarnawski, and Ve'\gh [J. ACM, 67 (2020), 37]. We improve on each part of this algorithm. We avoid the reduction to irreducible instances and thus obtain a simpler and much better reduction to vertebrate pairs. We also show that a slight variant of their algorithm for vertebrate pairs has a much smaller approximation ratio. Overall we improve the approximation ratio from 506 to 22 + \varepsilon for any \varepsilon > 0. This also improves the upper bound on the integrality ratio from 319 to 22.

关键词： traveling salesman problem approximation algorithms integrality ratio

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Minimizing the maximum lateness for scheduling with release times and job rejection

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JOURNAL OF COMBINATORIAL OPTIMIZATION 2024年第3期48卷 1-22页

作者： Kacem, Imed Kellerer, Hans Univ Lorraine LCOMS F-57000 Metz France Karl Franzens Univ Graz Inst Operat & Informat Syst A-8010 Graz Austria

We study scheduling problems with release times and rejection costs with the objective function of minimizing the maximum lateness. Our main result is a PTAS for the single machine problem with an upper bound on the rejection costs. This result is extended to parallel, identical machines. The corresponding problem of minimizing the rejection costs with an upper bound on the lateness is also examined. We show how to compute a PTAS for determining an approximation of the Pareto frontier on both objective functions on parallel, identical machines. Moreover, we present an FPTAS with strongly polynomial time for the maximum lateness problem without release times on identical machines when the number of machines is constant. Finally, we extend this FPTAS to the case of unrelated machines.

关键词： Scheduling Release times Lateness Rejection approximation algorithms

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Robust Gaussian Process Regression With Input Uncertainty: A PAC-Bayes Perspective

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IEEE TRANSACTIONS ON CYBERNETICS 2024年第2期54卷 962-973页

作者： Liu, Tianyu Lu, Jie Yan, Zheng Zhang, Guangquan Univ Technol Sydney Australian Artificial Intelligence Inst Sydney NSW 2007 Australia

The Gaussian process (GP) algorithm is considered as a powerful nonparametric-learning approach, which can provide uncertainty measurements on the predictions. The standard GP requires clearly observed data, unexpected perturbations in the input may lead to learned regression model mismatching. Besides, GP also suffers from the lack of good generalization performance guarantees. To deal with data uncertainty and provide a numerical generalization performance guarantee on the unknown data distribution, this article proposes a novel robust noisy input GP (NIGP) algorithm based on the probably approximately correct (PAC) Bayes theory. Furthermore, to reduce the computational complexity, we develop a sparse NIGP algorithm, and then develop a sparse PAC-Bayes NIGP approach. Compared with NIGP algorithms, instead of maximizing the marginal log likelihood, one can optimize the PAC-Bayes bound to pursue a tighter generalization error upper bound. Experiments verify that the NIGP algorithms can attain greater accuracy. Besides, the PAC-NIGP algorithms proposed herein can achieve both robust performance and improved generalization error upper bound in the face of both uncertain input and output data.

关键词： Training data Noise measurement approximation algorithms Gaussian processes Uncertainty Training Standards Bayesian learning Gaussian process (GP) probably approximately correct (PAC)-Bayes bound sparse approximation statistical learning

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