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arXiv 2025年

作者： Narayanan, Hariharan Srivastava, Piyush Tata Institute of Fundamental Research Maharashtra Mumbai India

Polynomial-time deterministic approximation of volumes of polytopes, up to an approximation factor that grows at most sub-exponentially with the dimension, remains an open problem. Recent work on this question has focused on identifying interesting classes of polytopes for which such approximation algorithms can be obtained. In this paper, we focus on one such class of polytopes: the Kostka polytopes. The volumes of Kostka polytopes appear naturally in questions of random matrix theory, in the context of evaluating the probability density that a random Hermitian matrix with fixed spectrum λ has a given diagonal μ (the so-called randomized Schur-Horn problem): the corresponding Kostka polytope is denoted GT(λ, μ). We give a polynomial-time deterministic algorithm for approximating the volume of a (Ω(n2) dimensional) Kostka polytope GT(λ, μ) to within a multiplicative factor of exp(O(n log n)), when λ is an integral partition with n parts, with entries bounded above by a polynomial in n, and μ is an integer vector lying in the interior of the permutohedron (i.e., convex hull of all permutations) of λ. The algorithm thus gives asymptotically correct estimates of the log-volume of Kostka polytopes corresponding to such (λ, μ). Our approach is based on a partition function interpretation of a continuous analogue of Schur polynomials. Copyright © 2025, The Authors. All rights reserved.

关键词： approximation algorithms

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Bilevel Optimization for Provisioning Heterogeneous Traffic in Deterministic Networks

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IEEE Transactions on Network and Service Management 2025年

作者： Zhu, Jing Wang, Dan Xing, Jiao Qin, Shuxin Tao, Gaofeng Chen, Pingping Zhu, Zuqing Purple Mountain Laboratories Jiangsu Nanjing211111 China University of Science and Technology of China School of Information Science and Technology Anhui Hefei230027 China

Due to the capabilities of providing extremely low packet loss and bounded end-to-end latency, deterministic networking (DetNet) has been considered as a promising technology for emerging time-sensitive applications (e.g., industrial control and smart grids) in IP networks. To provide deterministic services, the operator needs to address the routing and scheduling problem. In this work, we study the problem from a novel prospective, i.e., the problem should be optimized not only for deterministic traffic, but also for normal traffic to coexist with the former. Specifically, we redefine the problem as bandwidth allocation, routing and scheduling (BaRS), and model this problem as a bilevel optimization which consists of an upper-level optimization and a lower-level optimization. The upper-level optimization allocates link bandwidth between deterministic and normal traffic to maximize the available bandwidth for normal traffic on the premise of accepting a certain portion of deterministic bandwidth;the lower-level optimization determines specific routing and scheduling solutions for deterministic traffic to maximize the number of accepted deterministic flows. We first formulate the bilevel optimization as a bilevel mixed integer linear programming (BMILP). Then, we propose an exact algorithm based on cutting planes to solve it exactly, and propose an approximation algorithm based on two-level relaxations and randomized rounding to solve it effectively and time-efficiently. Extensive simulations are conducted and the results verify the effectiveness of our proposals in balancing the tradeoff between the available bandwidth for normal traffic and the number of accepted deterministic flows. © 2004-2012 IEEE.

关键词： approximation algorithms

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Fourth-Order Cumulant Based 3-D Near-Field Underdetermined Parameter Estimation With Exact Spatial Propagation Model

Fourth-Order Cumulant Based 3-D Near-Field Underdetermined P...

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International Conference on Acoustics, Speech, and Signal Processing (ICASSP)

作者： Longsheng Jin Hua Chen Jiaxiong Fang Wei Liu Ye Tian Gang Wang Faculty of Electrical Engineering and Computer Science Ningbo University China Department of Electrical and Electronic Engineering The Hong Kong Polytechnic University China

ISBN: (数字)9798350368741

ISBN: (纸本)9798350368758

Based on the exact spherical wavefront model, an under-determined estimation method for three-dimensional (3-D) parameters of near-field (NF) sources using L-shaped nested arrays is proposed, referred to as the cumulant algorithm. This algorithm leverages the temporal-spatial domain cumulants of NF sources by constructing virtual data through delayed fourth-order cumulant (FOC) calculations of the original received data. Subsequently, a spatial-spectrum-based subspace method is applied for 3-D NF localization, which involves a 3-D spectral search procedure. Additionally, the maximum number of identifiable NF sources of the proposed algorithm is analyzed. Simulation results demonstrate that, based on the exact spherical wavefront model, the proposed algorithm can achieve underdetermined 3-D parameter estimation of NF sources without any matching process, and it performs better in localization than existing methods.

关键词： Location awareness Solid modeling Three-dimensional displays Parameter estimation Simulation Signal processing algorithms Estimation approximation algorithms Noise measurement Speech processing

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A Construction of a Sequence of Feedback Controls for Discrete Control Problems Using Asymptotics

A Construction of a Sequence of Feedback Controls for Discre...

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International Russian Smart Industry Conference (SmartIndustryCon)

作者： Yulia Danik Mikhail Dmitriev Department 71 Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences Moscow Russia

ISBN: (数字)9798331511241

ISBN: (纸本)9798331511258

This paper explores the possibility of obtaining a symbolic description of a parametric family of synthesizing controls for nonlinear systems without control constraints using the Padé approximation method and the SDRE-based approach for control synthesis. On an example of a discrete optimal control problem with a positive parameter in the system dynamic equations an algorithm for constructing the first terms of a minimizing sequence of controls is proposed, where each term of the obtained control sequence is represented in the state feedback form. This construction is based on a set of neurons by which we understand various asymptotic approximations, Padé approximations (PA), and functions derived from them. Depending on a particular dynamic system a certain number of neurons will be used to get good quality approximation for the control. Asymptotic approximations and the PAs constructed on their basis capture the qualitative structure of the exact solution. Moreover, PAs can be improved through additional optimization procedures and modifications. The process of neurons selection, or activation, can be interpreted as a reinforcement learning algorithm in a certain neural network.

关键词： Training State feedback Regulators System dynamics Neurons Riccati equations Reinforcement learning Artificial neural networks approximation algorithms Feedback control

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Joint Transceiver Design and Mode Selection for NOMA-ISAC in NAFD Cell-Free mMIMO Systems

Joint Transceiver Design and Mode Selection for NOMA-ISAC in...

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International Conference on Communication Technology (ICCT)

作者： Jilong Wu Wei Jia Yiting Chen Pengcheng Zhu National Mobile Communication Research Laboratory Southeast University Nanjing P. R. China

ISBN: (数字)9798350363760

ISBN: (纸本)9798350363777

Integrated sensing and communication (ISAC) has garnered considerable attention for its capacity to simultaneously communicate and sense the surrounding environment. To enhance ISAC systems, non-orthogonal multiple access (NOMA) can be leveraged to mitigate interference between communication and sensing functions. This paper explores the transceiver design and mode selection for NOMA-ISAC in network-assisted fullduplex (NAFD) cell-free massive multiple-input multiple-output (mMIMO) systems. We firstly derive expressions for both the data rates of communication users and the sensing signal-to-interference-plus-noise ratios (SINRs) of radar targets. Subsequently, we formulate a joint optimization problem aimed at maximizing the sum sensing SINR while respecting communication constraints. To address this, we propose an algorithm based on sequential convex approximation (SCA) coupled with simulated annealing (SA) to obtain the optimal solution. Simulation results demonstrate the efficacy of our proposed algorithm in significantly enhancing system performance.

关键词： NOMA System performance Simulation Interference Radar Integrated sensing and communication approximation algorithms Transceivers Optimization Signal to noise ratio

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An Improved Grey Wolf Optimization Algorithm for Planting Structure Optimization in North China Mountainous Area

An Improved Grey Wolf Optimization Algorithm for Planting St...

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Artificial Intelligence, Human-Computer Interaction and Robotics (AIHCIR), International Conference on

作者： Yutong Gao Taohong Zhang School of Computer Science and Engineering Nanjing University of Science and Technology Nanjing China School of Computer and Communication Engineering University of Science and Technology Beijing Beijing China

ISBN: (数字)9798331534035

ISBN: (纸本)9798331534042

This study addresses the agricultural planting strategy optimization problem in North China's mountainous area by constructing three progressively in-depth mathematical models. These models consider factors such as planting restrictions, sales, and cost assumptions. An Improved Grey Wolf Optimization algorithm (IGWO) is proposed to solve the established mathematical models. Compared with the standard GWO algorithm, the particle swarm optimization (PSO) algorithm, and the differential evolution (DE) algorithm, the IGWO algorithm increases the economic benefits of agricultural planting structure by approximately 15%. Additionally, the ecological protection index is improved by 10%, and the social development index is increased by 8 %. This research provides a novel approach and perspective for optimizing agricultural planting structures.

关键词： Heuristic algorithms approximation algorithms Mathematical models Robustness Indexes Protection Particle swarm optimization Optimization Standards Robots

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Geometric Localization of Homology Cycles

arXiv

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arXiv 2024年

作者： Dhar, Amritendu Natarajan, Vijay Rathod, Abhishek Department of Computer Science and Automation Indian Institute of Science Bangalore India Zuse Institute Berlin Germany Department of Computer Science Ben Gurion University of the Negev

Computing an optimal cycle in a given homology class, also referred to as the homology localization problem, is known to be an NP-hard problem in general. Furthermore, there is currently no known optimality criterion that localizes classes geometrically and admits a stability property under the setting of persistent homology. We present a geometric optimization of the cycles that is computable in polynomial time and is stable in an approximate sense. Tailoring our search criterion to different settings, we obtain various optimization problems like optimal homologous cycle, minimum homology basis, and minimum persistent homology basis. In practice, the (trivial) exact algorithm is computationally expensive despite having a worst case polynomial runtime. Therefore, we design approximation algorithms for the above problems and study their performance experimentally. These algorithms have reasonable runtimes for moderate sized datasets and the cycles computed by these algorithms are consistently of high quality as demonstrated via experiments on multiple datasets. © 2024, CC BY.

关键词： approximation algorithms

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Beamforming Optimization of Secrecy Rate in Cognitive Radio Networks Assisted by STAR RIS

Beamforming Optimization of Secrecy Rate in Cognitive Radio ...

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International Conference on Computing, Networking and Communications (ICNC)

作者： Nian Liu Jia Hou School of Electronics & Information Soochow University Suzhou China

ISBN: (数字)9798331520960

ISBN: (纸本)9798331520977

The secure communication problem in spectrum-sharing underlay cognitive radio (CR) systems for secondary users (SU) is examined in the presence of multiple eavesdroppers (Eves). A novel approach employing a simultaneous transmitting and reflecting reconfigurable intelligent surface (STAR-RIS) is proposed to enhance the secrecy rate (SR) of SU. To address this, an alternating optimization (AO) algorithm based on successive convex approximation (SCA) and semi-definite relaxation (SDR) is developed. The transmit beamforming vectors at the base station (BS) and the phase shifts of the STAR-RIS are jointly optimized. The algorithm demonstrates efficient convergence to an optimal solution with a reduced number of iterations. Simulation results confirm a significant improvement in the secrecy rate of SU when compared to traditional RIS and combined RIS (CRIS) systems.

关键词： Base stations Array signal processing Simulation Stars Reconfigurable intelligent surfaces approximation algorithms Vectors Cognitive radio Optimization Convergence

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Secure Low-Complexity k-MCMC for Large-Scale Datasets with Fully Homomorphic Encryption

Secure Low-Complexity k-MCMC for Large-Scale Datasets with F...

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Information and Network Technologies (ICINT), International Conference on

作者： Shozo Saeki Minoru Kawahara Hirohisa Aman Center for Information Technology Ehime University Matsuyama Ehime Japan

ISBN: (数字)9798331536756

ISBN: (纸本)9798331536763

Outsourcing services and data sharing, such as artificial intelligence services and open science, have been increasing, and so has the importance of data security while keeping availability. One secure method is utilizing Fully Homomorphic Encryption (FHE). In addition, clustering algorithms with FHE have been proposed for outsourcing services. However, these algorithms are difficult to apply to a large-scale dataset due to FHE computations having high computational and space complexities. To address this, we propose secure low complexity k-MCMC (SLC k-MCMC), which approximate k-Means++ initialization and help clustering algorithms to fast convergence. SLC k-MCMC uses data packing with FHE and replaced sampling strategy (RSS), which reduces computational complexity and the amount of network traffic. Finally, we apply SLC k-MCMC to large-scale datasets, including million-scale datasets. As a result, SLC k-MCMC can be approximated to k-Means++ initialization with less than 1 / 1000th computational complexity and network traffic. Fast and high-quality initialization of SLC k-MCMC expands the applicability of the secure clustering algorithms to large-scale datasets.

关键词： Clustering algorithms Telecommunication traffic Big Data approximation algorithms Vectors Outsourcing Cryptography Homomorphic encryption Computational complexity Convergence

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Obfuscation of Node Centrality in Networks

Obfuscation of Node Centrality in Networks

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International Conference on Information Networking

作者： Hiroki Kawamura Ryotaro Matsuo Hiroyuki Ohsaki School of Engineering Kwansei Gakuin University Faculty of Engineering Fukuoka University

ISBN: (数字)9798331506940

ISBN: (纸本)9798331506957

Centrality measures determined by the network’s topology structure (e.g., degree centrality, eigenvector centrality, and betweenness centrality) are widely utilized in various fields, such as network analysis and data mining. While extensive research has proposed several centrality indices to measure how important a node is compared to others as well as fast centrality computation algorithms, there is a demand to obfuscate node centrality from a security and privacy perspective. Obfuscating node centrality offers potential applications, such as preventing attacks on important nodes from malicious actors. Therefore, this paper aims to develop an algorithm for obfuscating the centrality of arbitrary sets of nodes in a graph through the addition and deletion of links. Specifically, we introduce COBF (Centrality OBFuscation), which applies the concept of ProHiCo (Probabilistic algorithm to Hide Communities), a community obfuscation method proposed, to obfuscate node centrality. Experiments are conducted to analyze how effectively the centrality of specified nodes is obfuscated. The results demonstrate that COBF can effectively alter node rankings by approximately five positions in a network with a total of $\mathbf{1 0 0}$ nodes, highlighting its potential for enhancing privacy in network analysis.

关键词： Privacy Network topology Computational modeling Scalability Perturbation methods Network analyzers approximation algorithms Probabilistic logic Topology Velocity measurement

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