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A Structure-Driven Randomized Algorithm for the K-Center Problem

IEEE LATIN AMERICA TRANSACTIONS 2015年第3期13卷 746-752页

作者： Garcia, J. Menchaca, R. Menchaca, R. Quintero, R. Inst Politecn Nacl Ctr Invest Computac Mexico City DF Mexico

In this paper we present a new randomized approximation algorithm for the metric discrete k-center problem. The main idea is to apply random perturbations to the decisions made by a deterministic approximation algorithm in such a way as to keep the approximation guarantees with high probability, but at the same time explore an extended neighborhood of the solutions produced by the deterministic approximation algorithm. We formally characterize the proposed algorithm and show that it produces 2-approximated solutions with probability of at least 1 - 1/N when it is repeated at least alpha 1nN times. alpha, N is an element of Z(+) are user-defined parameters where a measures the size of the perturbations. Experimental results show that the proposed algorithm performs similar or better than a representative set of algorithms for the k-center problem and a GRASP algorithm, which is a popular state-of-the-art technique for randomizing deterministic algorithms. Our experiments also show that the quality of the solutions found by the proposed algorithm increases faster with the number of iterations and hence, is better suited for big instances where the execution of each iteration is very expensive.

关键词： k-center selection problem NP-Hard randomized algorithms approximation algorithms GRASP

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VARIABLE SIZED BIN PACKING

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SIAM JOURNAL ON COMPUTING 1986年第1期15卷 222-230页

作者： FRIESEN, DK LANGSTON, MA WASHINGTON STATE UNIV DEPT COMP SCIPULLMANWA 99164

In the classical bin packing problem one seeks to pack a list of pieces in the minimum space using unit capacity bins. This paper addresses the more general problem in which a fixed collection of bin sizes is allowed. Three efficient approximation algorithms are described and analyzed. They guarantee asymptotic worst-case performance bounds of 2,

3 / 2

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Fast vertex guarding for polygons with and without holes

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COMPUTATIONAL GEOMETRY-THEORY AND APPLICATIONS 2013年第3期46卷 219-231页

作者： King, James Imperial Coll London Dept Math London England

For a polygon P with n vertices, the vertex guarding problem asks for the minimum subset G of P's vertices such that every point in P is seen by at least one point in G. This problem is NP-complete and APX-hard. The first approximation algorithm (Ghosh, 1987) involves decomposing P into O(n(4)) cells that are equivalence classes for visibility from the vertices of P. This discretized problem can then be treated as an instance of SET COVER and solved in O(n(5)) time with a greedy O(log n)-approximation algorithm. Ghosh (2010) recently revisited the algorithm, noting that minimum visibility decompositions for simple polygons (Bose et al., 2000) have only O(n(3)) cells, improving the running time of the algorithm to O(n(4)) for simple polygons. In this paper we observe that, since minimum visibility decompositions for simple polygons have only O(n(2)) sinks (i.e., cells of minimal visibility) (Bose et al., 2000), the running time of the algorithm can be further improved to O(n(3)). We then extend the result of Bose et al. to polygons with holes, showing that a minimum visibility decomposition of a polygon with h holes has only O((h + 1)n(3)) cells and only O((h+1)(2)n(2)) cells of minimal visibility. We exploit this result to obtain a faster algorithm for vertex guarding polygons with holes. We then show that, in the same time complexity, we can attain approximation factors of O(log log OPT) for simple polygons and O((1 + log (h + 1)) log OPT) for polygons with holes. 2012 Elsevier B.V. All rights reserved.

关键词： Art gallery problem Vertex guarding approximation algorithms Visibility decomposition

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The Spiked Matrix Model With Generative Priors

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IEEE TRANSACTIONS ON INFORMATION THEORY 2021年第2期67卷 1156-1181页

作者： Aubin, Benjamin Loureiro, Bruno Maillard, Antoine Krzakala, Florent Zdeborova, Lenka Univ Paris Saclay Inst Phys Theor CNRS F-91190 Saclay France Univ Paris Saclay Inst Phys Theor CEA F-91190 Saclay France Ecole Polytech Federate Lausanne Informat Learning & Phys Lab CH-1015 Lausanne Switzerland Ecole Normale Super CNRS Lab Phys F-75006 Paris France Sorbonnes Univ F-75006 Paris France PSL Univ Ecole Normale Super F-75006 Paris France Ecole Polytech Federate Lausanne Stat Phys Computat Lab CH-1015 Lausanne Switzerland

We investigate the statistical and algorithmic properties of random neural-network generative priors in a simple inference problem: spiked-matrix estimation. We establish a rigorous expression for the performance of the Bayes-optimal estimator in the high-dimensional regime, and identify the statistical threshold for weak-recovery of the spike. Next, we derive a message-passing algorithm taking into account the latent structure of the spike, and show that its performance is asymptotically optimal for natural choices of the generative network architecture. The absence of an algorithmic gap in this case is in stark contrast to known results for sparse spikes, another popular prior for modelling low-dimensional signals, and for which no algorithm is known to achieve the optimal statistical threshold. Finally, we show that linearising our message passing algorithm yields a simple spectral method also achieving the optimal threshold for reconstruction. We conclude with an experiment on a real data set showing that our bespoke spectral method outperforms vanilla PCA.

关键词： Analytical models Principal component analysis Message passing approximation algorithms Mutual information Signal reconstruction Compressed sensing Signal processing algorithms principal component analysis (PCA) inverse problems statistical learning unsupervised learning

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POSITRON IMPACT EXCITATION OF THE N = 2 AND N = 3 MANIFOLDS OF HE IN THE RPA FORMULATION

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JOURNAL OF PHYSICS B-ATOMIC MOLECULAR AND OPTICAL PHYSICS 1992年第13期25卷 3037-3048页

作者： VARRACCHIO, EF PARCELL, LA MACQUARIE UNIV SCH MATH & PHYSN RYDENSW 2113AUSTRALIA

The random phase approximation formulation of the many-body Green function formalism is applied to inelastic transitions, in e+-atom scattering. Explicit numerical calculations are performed for excitation to the n = 2 and n = 3 manifolds of an He target. Theoretical results for excitation to the 2(1)P state are found to be in very good agreement with available experimental values of the literature, generally attributed to excitation of the 2(1)S level of He. It is further pointed out that the cross section for excitation of the 3(1)P level is, generally, bigger than that leading to the 2(1)S state and, possibly, within reach of present experimental sensitivity.

关键词： approximation algorithms

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Investigation of Enhanced Inertial Navigation algorithms by Functional Iteration

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IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS 2024年第5期60卷 7012-7022页

作者： Jiang, Hongyan Zhu, Maoran Wu, Yuanxin Shanghai Jiao Tong Univ Sch Elect Informat & Elect Engn Shanghai Key Lab Nav & Locat Based Serv Shanghai 200240 Peoples R China

The defects of the traditional strapdown inertial navigation algorithms become well acknowledged and the corresponding enhanced algorithms have been quite recently proposed trying to mitigate both theoretical and algorithmic defects. In this article, the analytical accuracy evaluation of both the traditional algorithms and the enhanced algorithms is investigated, against the true reference for the first time enabled by the functional iteration approach having provable convergence. The analyses by the help of MATLAB Symbolic Toolbox show that the resultant error orders of all algorithms under investigation are consistent with those in the existing literature, and the enhanced attitude algorithm notably reduces error orders of the traditional counterpart, while the impact of the enhanced velocity algorithm on error order reduction is insignificant. Simulation results agree with analyses that the superiority of the enhanced algorithm over the traditional one in the inertial attitude computation scenario diminishes significantly in the entire inertial navigation computation scenario, while the functional iteration approach possesses significant accuracy superiority even under sustained lowly dynamic conditions.

关键词： Vectors Heuristic algorithms approximation algorithms Inertial navigation Differential equations Polynomials Aerospace and electronic systems

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A Graph Classification Method Based on Support Vector Machines and Locality-Sensitive Hashing

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IEEE ACCESS 2024年 12卷 15791-15799页

作者： Gonzalez-Lima, Maria D. Ludena, Carenne C. Otazo-Sanchez, Gibran G. Univ North Dept Math & Stat Barranquilla 080003 Colombia Matrix CPM Solut Bogota 110231 Colombia BBVA AI Factory Mexico City 06600 Mexico

Graphs classification is a relevant problem that arises in many disciplines. Using graphs directly instead of vectorization allows exploiting the intrinsic representations of the data. Support Vector Machines (SVM) is a supervised learning method based on the use of graph kernel functions used for this task. One of the problems of SVM, as the number of samples increases, is the cost of storing and solving the optimization problem related to SVM. In this work, we propose a method capable of finding a small representative subset of the whole graph data set such that an approximate solution of the SVM optimization problem can be obtained in a fraction of the time, and without significantly degrading the classification prediction error. The method is based on the use of Locality-Sensitive Hashing for projecting over the Hilbert spaces defined by appropriate graph kernels that measure similarity between the graphs. A description of the algorithm, as well as numerical results using two graph kernels (Simple Product and Random Walk) on simulated and real life data sets are presented. The numerical experiments compare the training times and the classification error between the SVM obtained with our smart sampling approach, and the SVM obtained over the complete data set or over a random sub-sample. The results offer evidence of the advantages of our proposal for solving large scale graph classification problems when using SVM.

关键词： Support vector machines Training Optimization Hilbert space approximation algorithms Classification algorithms Graphical models Hash functions Graph classification locality sensitive hashing support vector machines

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Online multicasting in WDM networks with shared light splitter bank

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PHOTONIC NETWORK COMMUNICATIONS 2009年第1期17卷 1-9页

作者： Liu, Yuzhen Liang, Weifa Australian Natl Univ Dept Comp Sci Canberra ACT 0200 Australia

We study online multicasting in WDM networks with shared light splitter bank. Our objective is either to maximize the network throughput or to minimize the blocking probability. Due to the nature of dynamic requesting for network resources by online multicast requests, the network usually is unable to allocate the resources needed for each request in advance. Instead, it either accepts the request by building an economic multicast tree for the request, in terms of the utilization of the network resources if it has sufficient resources available, or rejects the request, otherwise. It is desirable that the cost of realizing each multicast request be minimized, and the network throughput will be maximized ultimately through the cost saving on each individual request. Since optical light splitting and wavelength conversion switching in optical networks is cost expensive and its fabrication is difficult, it is assumed that only a limited number of light splitters and wavelength converters are installed at a node, which will be shared by all the incoming signals at the node. In addition, it is further assumed that only a fraction of nodes in the network are installed with such optical switches. In this article we first propose a cost model for realizing an online multicast request under such network environments with limited light splitters and wavelength converters, which models the cost of utilization of network resources, particularly in modeling the light splitting and wavelength conversion ability at nodes. We then show that finding a cost-optimal multicast tree for a multicast request under the proposed cost model is NP-complete, and instead devise approximation and heuristic algorithms for it. We finally conduct experiments to evaluate the performance of the proposed algorithms. The results show that the proposed algorithms are efficient and effective in terms of network throughput.

关键词： Multicast Multicast routing and wavelength assignment Shared light splitter bank Optimal multicast trees WDM networks approximation algorithms Heuristic algorithms

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Rounding Algorithm of Minimizing Executing and Transmitting Time in Multiple CRANs

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IEEE ACCESS 2021年 9卷 166804-166814页

作者： Hu, Chia-Cheng Liu, Wen-Wu Pan, Jeng-Shyang Yango Univ Coll Artificial Intelligence Fuzhou 350015 Peoples R China Ningbo Univ Fac Elect Engn & Comp Sci Ningbo 315000 Zhejiang Peoples R China Shandong Univ Sci & Technol Coll Comp Sci & Engn Qingdao 266590 Peoples R China

Recently, Cloud Radio Access Network (CRAN) is a technology for reducing communication load and improving the performance of user tasks. In a CRAN, remote radio heads (RRHs) are densely set up to enable users to connect to the network nearby, and baseband unit (BBU) pools are used to store and execute user contents and tasks. In this paper, our goal is to perform joint optimization when scheduling user tasks and assigning RRH to users in a multiple CRAN infrastructure. The joint problem is NP-hard and modeled as a 0/1 integer linear programming (ILP) with the objective of minimizing the total time of executing user tasks and transmitting user output contents under the constraints of RRH linked capacities and BBU pool computing resources. Then, an algorithm is designed by adopting the rounding technology to solve the 0/1 ILP. We will prove its approximation ratio competitively. The conducted simulations further show that the difference between its solution and the optimal one of the 0/1 ILP is very small, and its approximation ratio is between 1.09 and 1.17. In the conducted experiments, the results demonstrate that the proposed algorithm is indeed practical to be implemented in a multiple CRAN infrastructure.

关键词： Task analysis Costs approximation algorithms Optimization Resource management Wireless communication Servers Cloud radio access network (CRAN) resource allocation task scheduling

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Scalable Approximate FRNN-OWA Classification

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IEEE TRANSACTIONS ON FUZZY SYSTEMS 2020年第5期28卷 929-938页

作者： Lenz, Oliver Urs Peralta, Daniel Cornelis, Chris Univ Ghent Dept Appl Math Comp Sci & Stat B-9000 Ghent Belgium Univ Ghent Data Min & Modelling Biomed Grp VIB Ctr Inflammat Res B-9000 Ghent Belgium

Fuzzy rough nearest neighbor classification with ordered weighted averaging operators (FRNN-OWA) is an algorithm that classifies unseen instances according to their membership in the fuzzy upper and lower approximations of the decision classes. Previous research has shown that the use of OWA operators increases the robustness of this model. However, calculating membership in an approximation requires a nearest neighbor search. In practice, the query time complexity of exact nearest neighbor search algorithms in more than a handful of dimensions is near linear, which limits the scalability of FRNN-OWA. Therefore, we propose approximate FRNN-OWA, a modified model that calculates upper and lower approximations of decision classes using the approximate nearest neighbors returned by hierarchical navigable small worlds (HNSW), a recent approximative nearest neighbor search algorithm with logarithmic query time complexity at constant near-100% accuracy. We demonstrate that approximate FRNN-OWA is sufficiently robust to match the classification accuracy of exact FRNN-OWA while scaling much more efficiently. We test four parameter configurations of HNSW and evaluate their performance by measuring classification accuracy and construction and query times for samples of various sizes from three large datasets. We find that with two of the parameter configurations, approximate FRNN-OWA achieves near-identical accuracy to exact FRNN-OWA for most sample sizes within query times that are up to several orders of magnitude faster.

关键词： Open wireless architecture Rough sets Training Time complexity approximation algorithms Machine learning algorithms Fuzzy systems Big data applications classification algorithms fuzzy rough sets nearest neighbor searches scalability

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