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31st International Colloquium on Structural Information and Communication Complexity (SIROCCO)

作者： Halldorsson, Magnus M. Rawitz, Dror Reykjavik Univ Dept Comp Sci Reykjavik Iceland Bar Ilan Univ Faulty Engn Ramat Gan Israel

ISBN: (纸本)9783031606021;9783031606038

We consider the Maximum WEIGHT INDEPENDENT SET problem, with a focus on obtaining good approximations for graphs of small maximum degree Delta. We give deterministic local algorithms running in time poly(Delta, log n) that come close to matching the best centralized results known and improve the previous distributed approximations by a factor of about 2. More precisely, we obtain approximations below Delta+1/2/2, and a further improvement to 8/5 + epsilon when Delta = 3. Technically, this is achieved by leveraging the fractional local ratio technique, for a first application in a distributed setting.

关键词： approximation algorithms

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approximation algorithms for optimization problems in random power-law graphs

Lecture Notes in Computer Science (including subseries Lectu...

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Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 2014年 8881卷 343-355页

作者： Shen, Yilin Li, Xiang Thai, My T. Samsung Research America San JoseCA95134 United States CISE Department University of Florida GainesvilleFL32611 United States

Many large-scale real-world networks are well-known to have the power law distribution in their degree sequences: the number of vertices with degree i is proportional to i-βfor some constant β. It is a common belief that solving optimization problems in power-law graphs is easier. Unfortunately, many problems have been proven NP-hard, along with their inapproximability factors in power-law graphs. Therefore, it is of great importance to develop an algorithm framework such that these optimization problems can be approximated in power-law graphs, with provable theoretical approximation ratios. In this paper, we propose an algorithmic framework, called Low-Degree Percolation (LDP) Framework, for solving Minimum Dominating Set, Minimum Vertex Cover and Maximum Independent Set problems in power-law graphs. Using this framework, we further show a theoretical framework to derive the approximation ratios for these optimization problems in two well-known random power-law graphs. Our numerical analysis shows that, these optimization problems can be approximated into near 1 factor with high probability, using our proposed LDP algorithms, in power-law graphs with exponential factor β ≥ 1.5, which belongs to the range of most real-world networks. © Springer International Publishing Switzerland 2014.

关键词： approximation algorithms

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A Hierarchical OPF Algorithm With Improved Gradient Evaluation in Three-Phase Networks

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IEEE TRANSACTIONS ON CONTROL OF NETWORK SYSTEMS 2025年第1期12卷 825-837页

作者： Liang, Heng Zhou, Xinyang Zhao, Changhong Chinese Univ Hong Kong Dept Informat Engn Hong Kong Peoples R China Natl Renewable Energy Lab Golden CO 80401 USA

Linear approximation commonly used in solving ac optimal power flow (OPF) simplifies the system models but incurs accumulated voltage errors in large power networks. Such errors will make the primal-dual type gradient algorithms converge to solutions with voltage violations. In this article, we improve a recent hierarchical OPF algorithm that rested on primal-dual gradients evaluated with a linearized distribution power flow model. Specifically, we propose a more accurate gradient evaluation method based on an unbalanced three-phase nonlinear distribution power flow model to mitigate the errors arising from linearization. The resultant gradients feature a blocked structure that enables our development of an improved hierarchical primal-dual algorithm to solve the OPF problem. Numerical results on the IEEE 123-bus test feeder and a 4518-node test feeder show that the proposed method can enhance voltage safety at comparable computational efficiency with the linearized algorithm.

关键词： Load flow approximation algorithms Vectors Network systems Control systems Computational modeling Voltage control Distributed algorithm optimal power flow (OPF) unbalanced three-phase networks voltage control

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Exponential-Time approximation Schemes via Compression 15

Exponential-Time Approximation Schemes via Compression

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15th Innovations in Theoretical Computer Science Conference (ITCS)

作者： Inamdar, Tanmay Kundu, Madhumita Parviainen, Pekka Ramanujan, M. S. Saurabh, Saket Indian Inst Technol Jodhpur Rajasthan India Univ Bergen Bergen Norway Univ Warwick Coventry W Midlands England Inst Math Sci Chennai Tamil Nadu India

ISBN: (纸本)9783959773096

In this paper, we give a framework to design exponential-time approximation schemes for basic graph partitioning problems such as k-WAY CUT, MULTIWAY CUT, STEINER k-CUT and MULTICUT, where the goal is to minimize the number of edges going across the parts. Our motivation to focus on approximation schemes for these problems comes from the fact that while it is possible to solve them exactly in 2nn (1) time (note that this is already faster than brute-forcing over all partitions or edge sets), it is not known whether one can do better. Using our framework, we design the first (1 + 0 -approximation algorithms for the above problems that run in time 2f(')' (for f (6) < 1) for all these problems. As part of our framework, we present two compression procedures. The first of these is a "lossless" procedure, which is inspired by the seminal randomized contraction algorithm for Global Min-cut of Karger [SODA '93]. Here, we reduce the graph to an equivalent instance where the total number of edges is linearly bounded in the number of edges in an optimal solution of the original instance. Following this, we show how a careful combination of greedy choices and the best exact algorithm for the respective problems can exploit this structure and lead to our approximation schemes. Our first compression procedure bounds the number of edges linearly in the optimal solution, but this could still leave a dense graph as the solution size could be superlinear in the number of vertices. However, for several problems, it is known that they admit significantly faster algorithms on instances where solution size is linear in the number of vertices, in contrast to general instances. Hence, a natural question arises here. Could one reduce the solution size to linear in the number of vertices, at least in the case where we are willing to settle for a near-optimal solution, so that the aforementioned faster algorithms could be exploited? In the second compression procedure, using cut sparsifiers

关键词： Exponential-Time algorithms approximation algorithms Graph algorithms Cut Problems

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Heavy Nodes in a Small Neighborhood: Exact and Peeling algorithms With Applications

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IEEE TRANSACTIONS ON KNOWLEDGE AND DATA ENGINEERING 2025年第4期37卷 1853-1870页

作者： Li, Ling Verbeek, Hilde Chen, Huiping Loukides, Grigorios Gwadera, Robert Stougie, Leen Pissis, Solon P. Kings Coll London Dept Informat London WC2B 4BG England Ctr Wiskunde & Informat CWI NL-1098 XG Amsterdam Netherlands Univ Birmingham Birmingham B15 2TT England UBS AG CH-4051 Basel Switzerland CWI NL-1081 HV Amsterdam Netherlands Vrije Univ NL-1081 HV Amsterdam Netherlands

We introduce a weighted and unconstrained variant of the well-known minimum k union problem: Given a bipartite graph G(U,V,E) with weights for all nodes in V, find a set S subset of V such that the ratio between the total weight of the nodes in S and the number of their distinct adjacent nodes in U is maximized. Our problem, which we term Heavy Nodes in a Small Neighborhood (HNSN), finds applications in marketing, team formation, and money laundering detection. For example, in the latter application, S represents bank account holders who obtain illicit money from some peers of a criminal and route it through their accounts to a target account belonging to the criminal. We prove that HNSN can be solved exactly in polynomial time via linear programming. We also develop several algorithms offering different effectiveness/efficiency trade-offs: an exact algorithm, based on node contraction, graph decomposition, and linear programming, as well as three peeling algorithms. The first peeling algorithm is a near-linear time approximation algorithm with a tight approximation ratio, the second is an iterative algorithm that converges to an optimal solution in a very small number of iterations in practice, and the third is a near-linear time greedy heuristic. In addition, we formalize a money laundering scenario involving multiple target accounts and show how our algorithms can be extended to deal with it. Our experiments on real and synthetic datasets show that our algorithms find (near-)optimal solutions, outperforming a natural baseline, and that they can detect money laundering more effectively and efficiently than two state-of-the-art methods.

关键词： Peer-to-peer computing approximation algorithms Heuristic algorithms IP networks Flowering plants Bipartite graph Linear programming Polynomials Optimization Glass Minimum k union dense subgraph discovery combinatorial optimization money laundering detection

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Improved Turbo Message Passing for Compressive Robust Principal Component Analysis: Algorithm Design and Asymptotic Analysis

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IEEE TRANSACTIONS ON INFORMATION THEORY 2025年第2期71卷 1323-1361页

作者： He, Zhuohang Ma, Junjie Yuan, Xiaojun Univ Elect Sci & Technol China Natl Key Lab Wireless Commun Chengdu 611731 Peoples R China Chinese Acad Sci Acad Math & Syst Sci Inst Computat Math & Sci Engn Comp Beijing 100864 Peoples R China

- Compressive Robust Principal Component Analysis (CRPCA) naturally arises in various applications as a means to recover a low-rank matrix low-rank matrix L and a sparse matrix S from compressive measurements. In this paper, we approach the problem from a Bayesian inference perspective. We establish a probabilistic model for the problem and develop an improved turbo message passing (ITMP) algorithm based on the sum-product rule and the appropriate approximations. Additionally, we establish a state evolution framework to characterize the asymptotic behavior of the ITMP algorithm in the large-system limit. By analyzing the established state evolution, we further propose sufficient conditions for the global convergence of our algorithm. Our numerical results validate the theoretical results, demonstrating that the proposed asymptotic framework accurately characterize the dynamical behavior of the ITMP algorithm, and the phase transition curve specified by the sufficient condition agrees well with numerical simulations

关键词： Sparse matrices Bayes methods approximation algorithms Principal component analysis Message passing Inference algorithms Heuristic algorithms Convergence Face recognition Noise measurement Robust PCA compressed sensing approximate message passing state evolution low-rank matrix denoising singular value thresholding random matrix theory phase transition

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Prescribed Performance Robust Approximate Optimal Tracking Control via Stackelberg Game

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IEEE TRANSACTIONS ON AUTOMATION SCIENCE AND ENGINEERING 2025年 22卷 12871-12883页

作者： Tan, Junkai Xue, Shuangsi Li, Huan Guo, Zihang Cao, Hui Li, Dongyu Xi An Jiao Tong Univ Shaanxi Key Lab Smart Grid Xian 710049 Peoples R China Xi An Jiao Tong Univ Sch Elect Engn State Key Laboratoryof Elect Insulat & Power Equip Xian 710049 Peoples R China Beihang Univ Sch Cyber Sci & Technol Beijing 100191 Peoples R China

Real-world applications of nonlinear systems tracking control are always challenging due to the existence of uncertainties and disturbances. To design a robust optimal tracking controller for uncertain nonlinear systems with disturbances and actuator saturation, this paper investigates the prescribed performance robust optimal tracking control problem. A prescribed performance mechanism is constructed to convert the dynamics of tracking error into transformed error dynamics, which keeps the system's operating states within specific bounds, ensuring tracking with predefined error constraints. For the optimal tracking controller design, an optimal index is established to optimize the performance of tracking control, and a robust optimal index is established to optimize the disturbance effect on the tracking error. To achieve robust optimal tracking control that minimizes both optimal and robust optimal indexes, a Stackelberg game is constructed, which provides a hierarchical game structure for the optimal controller and the worst disturbance. The robust optimal controller is approximated online using reinforcement learning techniques. An actor-critic-identifier algorithm is designed to approximate the optimal value function, optimal controller, and drifted system parameters. Lyapunov theory is utilized to analyze the closed-loop system's stability. To demonstrate the effectiveness of the proposed robust optimal control method, two numerical simulations and a hardware experiment on a quadcopter system are conducted. The experiment results demonstrate that our method successfully achieves prescribed performance tracking control when actuators are saturated and disturbances are present. Note to Practitioners-In this paper, the probelm of mixed H-2/H-infinity prescribed-performance optimal tracking control for nonlinear systems with input saturation is investigated. To constrain the operating states of the system within certain bounds, the prescribed performance transform

关键词： Insulation life Degradation Indexes Games Nonlinear dynamical systems Trajectory Robustness Actuators approximation algorithms Uncertainty Prescribed performance control Stackelberg game approximate optimal control actor-critic system identification

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A Constant-Factor approximation for Nash Social Welfare with Subadditive Valuations 2024

A Constant-Factor Approximation for Nash Social Welfare with...

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56th Annual ACM Symposium on Theory of Computing (STOC)

作者： Dobzinski, Shahar Li, Wenzheng Rubinstein, Aviad Vondrak, Jan Weizmann Inst Sci Rehovot Israel Stanford Univ Stanford CA 94305 USA

ISBN: (纸本)9798400703836

We present a constant-factor approximation algorithm for the Nash Social Welfare (NSW) maximization problem with subadditive valuations accessible via demand queries. More generally, we propose a framework for NSW optimization which assumes two subroutines that (1) solve a configuration-type LP under certain additional conditions, and (2) round the fractional solution with respect to utilitarian social welfare. In particular, a constant-factor approximation for submodular valuations with value queries can also be derived from our framework.

关键词： Nash Social Welfare approximation algorithms Combinatorial Optimization

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A Simple (1-ε)-approximation Semi-Streaming Algorithm for Maximum (Weighted) Matching 7

A Simple (1-ε)-Approximation Semi-Streaming Algorithm for M...

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Symposium on Simplicity in algorithms (SOSA)

作者： Assadi, Sepehr Univ Waterloo Cheriton Sch Comp Sci Waterloo ON Canada Rutgers State Univ Dept Comp Sci New Brunswick NJ 08901 USA

ISBN: (纸本)9781611977936

We present a simple semi-streaming algorithm for (1 - epsilon)-approximation of bipartite matching in O (log(n)=epsilon) passes. This matches the performance of state-of-the-art "epsilon-efficient" algorithms-the ones with much better dependence on epsilon albeit with some mild dependence on n|while being considerably simpler. The algorithm relies on a direct application of the multiplicative weight update method with a self-contained primal-dual analysis that can be of independent interest. To show case this, we use the same ideas, alongside standard tools from matching theory, to present an equally simple semi-streaming algorithm for (1 - epsilon)approximation of weighted matchings in general (not necessarily bipartite) graphs, again in O (log(n)/epsilon) passes.

关键词： approximation algorithms

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Learning From Demonstrations: A Computationally Efficient Inverse Reinforcement Learning Approach With Simplified Implementation

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IEEE TRANSACTIONS ON EMERGING TOPICS IN COMPUTATIONAL INTELLIGENCE 2025年

作者： Lin, Yanbin Ni, Zhen Zhong, Xiangnan Florida Atlantic Univ Dept Elect Engn & Comp Sci Boca Raton FL 33431 USA

Reinforcement learning (RL) research usually requires a reward function from sophisticated domain knowledge to perform well. Inverse reinforcement learning (IRL) methods provide the opportunity to recover such reward functions from existing expert demonstrations. However, current IRL methods require intensive computation and excessive memory storage when the state space increases. To this end, we propose a computationally efficient inverse reinforcement learning (e-IRL) approach to 1) simplify the gradient algorithm for the reward network;2) implement the loss function with feature expectation instead of state visiting frequency;and 3) enable fast, accurate, and automatic feature processing. Specifically, we design a new featurization network to accommodate trajectories and automatically output the aligned feature vectors without human intervention. In addition, this proposed approach derives simplified algorithm formulas to obtain a gradient of loss function to update weights for the reward network. This approach eliminates repeated calculation and excessive storage of gradient parameters from demonstrated trajectories in literature. The feature expectation computation for both the expert (one-shot) and learner (streamlined) is employed to efficiently obtain the important gradient parameters. Three examples are considered to validate the effectiveness of the proposed method, which shows better performance in terms of average return, required average number of steps, and required number of demonstrations than comparable methods.

关键词： Trajectory Reinforcement learning Training Optimization Heuristic algorithms approximation algorithms Markov decision processes Iterative methods Imitation learning Computational modeling Actor critic methods inverse reinforcement learning neural networks reward recovering featurization network and online optimization

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