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A Low Complexity DOA Estimation Method of CD Sources in Impulsive Noise

IEEE ACCESS 2021年 9卷 142857-142868页

作者： Cai, Ruiyan Tian, Quan Qiu, Tianshuang Taizhou Univ Sch Elect & Informat Engn Taizhou 318000 Peoples R China Dalian Univ Technol Fac Elect Informat & Elect Engn Dalian 116024 Peoples R China

Direction of arrival (DOA) estimation, as the main technology of passive radio monitoring and positioning, has been deeply investigated. However, the DOA for distributed sources is challenging to estimate in environments with impulsive noise. Although many methods have been proposed for DOA estimation, most of them assume that array output signals contain Gaussian noise. Therefore, the performance of these methods is often poor for alpha-stable distributed impulsive noise. Furthermore, subspace-based DOA estimation methods for distributed sources require a two-dimensional (2D) peak search, which increases the consumption of system computing resources. In this paper, a Q-function-based kernel function is proposed, and its properties are derived. On this basis, a novel DOA estimation method is proposed for coherently distributed (CD) sources in impulsive noise. To reduce computational complexity, a Lagrangian quadratic optimization function is derived by approximating the generalized array manifold of the CD source. By solving this optimization function, a 2D peak search can be reduced to several one-dimensional (1D) peak searches. The simulation results illustrate that the accuracy and robustness of the proposed method outperform those of existing methods.

关键词： Direction-of-arrival estimation Estimation Multiple signal classification Computational complexity approximation algorithms Optimization Manifolds DOA estimation distributed sources impulsive noise alpha-stable distribution

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On the parameterized complexity of computing tree-partitions

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Discrete Mathematics and Theoretical Computer Science 2025年 263卷

作者： Bodlaender, Hans L. Groenland, Carla Jacob, Hugo Universiteit Utrecht Utrecht Netherlands Technische Universiteit Delft Delft Netherlands LIRMM Université de Montpellier CNRS Montpellier France

We study the parameterized complexity of computing the tree-partition-width, a graph parameter equivalent to treewidth on graphs of bounded maximum degree. On one hand, we can obtain approximations of the tree-partition-width efficiently: we show that there is an algorithm that, given an n-vertex graph G and an integer k, constructs a tree-partition of width O(k7) for G or reports that G has tree-partition-width more than k, in time kO(1)n2. We can improve slightly on the approximation factor by sacrificing the dependence on k, or on n. On the other hand, we show the problem of computing tree-partition-width exactly is XALP-complete, which implies that it is W[t]-hard for all t. We deduce XALP-completeness of the problem of computing the domino treewidth. Next, we adapt some known results on the parameter tree-partition-width and the topological minor relation, and use them to compare tree-partition-width to tree-cut width. Finally, for the related parameter weighted tree-partition-width, we give a similar approximation algorithm (with ratio now O(k15)) and show XALP-completeness for the special case where vertices and edges have weight 1. © 2024 by the author(s)

关键词： approximation algorithms

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A Polyhedral Annexation Algorithm for Aligning Partially Overlapping Point Sets

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IEEE ACCESS 2021年 9卷 166750-166761页

作者： Lian, Wei Zuo, Wangmeng Cui, Zhesen Changzhi Univ Dept Comp Sci Changzhi 046011 Shanxi Peoples R China Harbin Inst Technol Sch Comp Sci & Technol Harbin 150001 Peoples R China

Point set registration aims to find a spatial transformation that best aligns two point sets. algorithms which can handle partial overlap and are invariant to the corresponding transformations are particularly desirable. To this end, we first reduce the objective of the robust point matching (RPM) algorithm to a function of a low dimensional variable. The resulting function is nevertheless only concave over a finite region including the feasible region, which prohibits the use of the popular branch-and-bound (BnB) algorithm. To address this issue, we propose to use the polyhedral annexation (PA) algorithm for optimization, which enjoys the merit of only operating within the concavity region of the objective function. The proposed algorithm does not need regularization on transformation and thus is invariant to the corresponding transformation. It is also approximately globally optimal and thus is guaranteed to be robust. Moreover, its most computationally expensive subroutine is a linear assignment problem which can be efficiently solved. Experimental results demonstrate better robustness of the proposed method over the state-of-the-art algorithms. Our method's matching error is on average 44% (resp. 65%) lower than that of Go-ICP in 2D (resp. 3D) synthesized tests. It is also efficient when the number of transformation parameters is small.

关键词： Optimization Symmetric matrices Three-dimensional displays Feature extraction approximation algorithms Robustness Matrix converters Point set registration branch-and-bound concave optimization polyhedral annexation

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A Parallel Structured Divide-and-Conquer Algorithm for Symmetric Tridiagonal Eigenvalue Problems

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IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS 2021年第2期32卷 367-378页

作者： Liao, Xia Li, Shengguo Lu, Yutong Roman, Jose E. Natl Univ Def Technol Coll Comp Sci Changsha Peoples R China Sun Yatsen Univ Natl Supercomp Ctr Guangzhou Guangzhou 510006 Peoples R China Sun Yatsen Univ Sch Data & Comp Sci Guangzhou 510006 Peoples R China Univ Politecn Valencia D Sistemes Informat & Comp Canu Vera S-N Valencia 46022 Spain

In this article, a parallel structured divide-and-conquer (PSDC) eigensolver is proposed for symmetric tridiagonal matrices based on ScaLAPACK and a parallel structured matrix multiplication algorithm, called PSMMA. Computing the eigenvectors via matrix-matrix multiplications is the most computationally expensive part of the divide-and-conquer algorithm, and one of the matrices involved in such multiplications is a rank-structured Cauchy-like matrix. By exploiting this particular property, PSMMA constructs the local matrices by using generators of Cauchy-like matrices without any communication, and further reduces the computation costs by using a structured low-rank approximation algorithm. Thus, both the communication and computation costs are reduced. Experimental results show that both PSMMA and PSDC are highly scalable and scale to 4096 processes at least. PSDC has better scalability than PHDC that was proposed in [16] and only scaled to 300 processes for the same matrices. Comparing with PDSTEDC in ScaLAPACK, PSDC is always faster and achieves 1.4x-1.6x speedup for some matrices with few deflations. PSDC is also comparable with ELPA, with PSDC being faster than ELPA when using few processes and a little slower when using many processes.

关键词： approximation algorithms Symmetric matrices Generators Eigenvalues and eigenfunctions Matrix decomposition Complexity theory Scalability PSMMA PUMMA algorithm ScaLAPACK divide-and-conquer rank-structured matrix cauchy-like matrix

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An Improved approximation Bound for Minimum Weight Dominating Set on Graphs of Bounded Arboricity 19th

An Improved Approximation Bound for Minimum Weight Dominatin...

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19th International Workshop on approximation and Online algorithms, WAOA 2021

作者： Sun, Hao University of Waterloo WaterlooONN2L 3G1 Canada

ISBN: (纸本)9783030927011

We consider the minimum weighted dominating set problem on graphs having bounded arboricity. We show that the natural LP has an integrality gap of at most one more than the arboricity of our graph via a primal-dual algorithm. This is nearly the best approximation possible, as Bansal and Umboh have shown it is NP-hard to approximate dominating sets to within one less than the arboricity of the graph. © 2021, Springer Nature Switzerland AG.

关键词： approximation algorithms

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Improved approximation for longest common subsequence over small alphabets 48

Improved approximation for longest common subsequence over s...

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48th International Colloquium on Automata, Languages, and Programming, ICALP 2021

作者： Akmal, Shyan Williams, Virginia Vassilevska MIT EECS CSAIL CambridgeMA United States

ISBN: (纸本)9783959771955

This paper investigates the approximability of the Longest Common Subsequence (LCS) problem. The fastest algorithm for solving the LCS problem exactly runs in essentially quadratic time in the length of the input, and it is known that under the Strong Exponential Time Hypothesis the quadratic running time cannot be beaten. There are no such limitations for the approximate computation of the LCS however, except in some limited scenarios. There is also a scarcity of approximation algorithms. When the two given strings are over an alphabet of size k, returning the subsequence formed by the most frequent symbol occurring in both strings achieves a 1/k approximation for the LCS. It is an open problem whether a better than 1/k approximation can be achieved in truly subquadratic time (O(n2.δ) time for constant δ > 0). A recent result [Rubinstein and Song SODA'2020] showed that a 1/2 + ∈ approximation for the LCS over a binary alphabet is possible in truly subquadratic time, provided the input strings have the same length. In this paper we show that if a 1/2 + ∈ approximation (for ∈ > 0) is achievable for binary LCS in truly subquadratic time when the input strings can be unequal, then for every constant k, there is a truly subquadratic time algorithm that achieves a 1/k + δ approximation for k-ary alphabet LCS for some δ > 0. Thus the binary case is the hardest. We also show that for every constant k, if one is given two strings of equal length over a k-ary alphabet, one can obtain a 1/k + ∈ approximation for some constant ∈ > 0 in truly subquadratic time, thus extending the Rubinstein and Song result to all alphabets of constant size. © 2021 Shyan Akmal and Virginia Vassilevska Williams.

关键词： approximation algorithms

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Routing-Oblivious Network-Wide Measurements

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IEEE-ACM TRANSACTIONS ON NETWORKING 2021年第6期29卷 2386-2398页

作者： Ben-Basat, Ran Einziger, Gil Feibish, Shir Landau Moraney, Jalil Tayh, Bilal Raz, Danny UCL Dept Comp Sci London NW1 2AE England Ben Gurion Univ Negev Dept Comp Sci IL-8410501 Beer Sheva Israel Open Univ Israel IL-4353701 Raanana Israel Technion Israel Inst Technol Dept Comp Sci IL-3200003 Haifa Israel

The recent introduction of SDN allows deploying new centralized network algorithms that dramatically improve network operations. In such algorithms, the centralized controller obtains a network-wide view by merging measurement data from Network Measurement Points (NMPs). A fundamental challenge is that several NMPs may count the same packet, reducing the accuracy of the measurement. Existing solutions circumvent this problem by assuming that each packet traverses a single NMP or that the routing is fixed and known. This work suggests novel algorithms for three fundamental network-wide measurement problems without making any assumptions on the topology and routing and without modifying the underlying traffic. Specifically, this work introduces two algorithms for estimating the number of (distinct) packets or byte volume in the measurement, estimating per-flow packet and byte counts, and finding the heavy hitter flows. Our work includes formal accuracy guarantees and an extensive evaluation consisting of the realistic fat-tree topology and three real network traces. Our evaluation shows that our algorithms outperform existing works and provide accurate measurements within reasonable space parameters.

关键词： Routing Topology Network topology Monitoring approximation algorithms Computer science Weight measurement Communication technology communication systems computer networks Internet

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Multi-Objective Deep Reinforcement Learning Assisted Service Function Chains Placement

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IEEE TRANSACTIONS ON NETWORK AND SERVICE MANAGEMENT 2021年第4期18卷 4134-4150页

作者： Bi, Yu Meixner, Carlos Colman Bunyakitanon, Monchai Vasilakos, Xenofon Nejabati, Reza Simeonidou, Dimitra Univ Bristol Fac Engn Sch Comp Sci Elect & Elect Engn & Engn Maths SCEE Smart Internet LabHigh Performance Networks Grp Bristol BS8 1QU Avon England

The study of Service Function Chains (SFCs) placement problem is crucial to support services flexibly and use resources efficiently. Solutions should satisfy various Quality of Service requirements, avoid edge resource congestion, and improve service acceptance ratio (SAR). This work presents a novel approach to address these challenges by solving a multi-objective SFCs placement problem based on the Pointer Network in multi-layer edge and cloud networks. We design a Deep Reinforcement Learning algorithm, called Chebyshev-assisted Actor-Critic SFCs Placement Algorithm, to overcome the limitations of traditional heuristic and evolutionary algorithms. Then, we run this algorithm iteratively with a set of weights to obtain non-dominated fronts, which have much higher hypervolume values than those obtained from other state-of-the-art algorithms. Moreover, running our algorithm individually with selected weights from non-dominated fronts can avoid edge resource congestion and achieve 98% SARs of low-latency services during high-workload periods. Finally, based on both simulation and real testbed experimental results, it is validated that the proposed algorithm fits for pragmatic service deployment while achieving 100% of SARs in the use cases deployed on the testbed.

关键词： Heuristic algorithms Cloud computing Quality of service Optimization Computational modeling approximation algorithms Costs Network function virtualisation service function chaining multi-objective deep reinforcement learning multi-access edge computing optical network

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Optimal l1 column subset selection and a fast PTAS for low rank approximation 32

Optimal l1 column subset selection and a fast PTAS for low r...

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32nd Annual ACM-SIAM Symposium on Discrete algorithms, SODA 2021

作者： Mahankali, Arvind V. Woodruff, David P. Carnegie Mellon University

ISBN: (纸本)9781611976465

We study the problem of entrywise l1 low rank approximation. We give the first polynomial time column subset selection-based l1 low rank approximation algorithm sampling Oe(k) columns and achieving an Oe(k1/2)approximation for any k, improving upon the previous best Oe(k)-approximation and matching a prior lower bound for column subset selection-based l1-low rank approximation which holds for any poly(k) number of columns. We extend our results to obtain tight upper and lower bounds for column subset selection-based lp low rank approximation for any 1 p low rank approximation of an n×d matrix, for 1 ≤ p n×d, returns a rank-k matrix Ab in 2poly(k/Ε) + poly(nd) running time that achieves the following guarantee: kA− Abkp ≤ (1 + Ε) · OPT + poly(Εk)kAkp where OPT = minAkrank k kA−Akkp. Using this algorithm, in the same running time we give an algorithm which obtains error at most (1 + Ε) · OPT and outputs a matrix of rank at most 3k - these algorithms significantly improve upon all previous (1 + Ε)- and O(1)-approximation algorithms for the lp low rank approximation problem, which required at least npoly(k/Ε) or npoly(k) running time, and either required strong bit complexity assumptions (our algorithms do not) or had bicriteria rank 3k. Finally, we show hardness results which nearly match our 2poly(k)+poly(nd) running time and the above additive error guarantee. Copyright © 2021 by SIAM

关键词： approximation algorithms

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Fully Dynamic Clustering and Diversity Maximization in Doubling Metrics

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ACM Transactions on Knowledge Discovery from Data 2025年第4期19卷

作者： Pellizzoni, Paolo Pietracaprina, Andrea Pucci, Geppino Max Planck Institute of Biochemistry Martinsried Germany University of Padova Padova Italy

We present approximation algorithms for some variants of k-center clustering and diversity maximization in a fully dynamic setting, where the active pointset evolves through arbitrary insertions and deletions. All algorithms employ a coreset-based strategy and rely on the use of the cover tree data structure, which we crucially augment to maintain, at any time, some additional information enabling the efficient extraction of the solution for the specific problem. For all the problems under consideration, our algorithms compute (α+ϵ)-approximate solutions, where is the best-known approximation attainable in polynomial time in the standard static setting, and ϵ > 0 is a user-provided accuracy parameter. Remarkably, and unlike previous works, the (cover tree) data structure used by our algorithms and the running times of the update procedures are both independent of the accuracy parameter and, for the k-center variants, also of parameter k. The analysis is performed in terms of the doubling dimension of the metric space which the points belong to, and it shows that, for spaces of bounded doubling dimension, the times required to extract solutions to the above problems are dramatically smaller than those that would be required to recompute solutions on the entire active pointset from scratch. To the best of our knowledge, ours are the first solutions for the matroid center and diversity maximization problems in the fully dynamic setting. The theoretical results are complemented by an extensive set of experiments, which demonstrate the efficiency and effectiveness of our algorithms for k-center without and with outliers against previously known ones. © 2025 Copyright held by the owner/author(s).

关键词： approximation algorithms

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