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AN O(N) ALGORITHM FOR THE linear MULTIPLE-CHOICE KNAPSACK-PROBLEM AND RELATED PROBLEMS

INFORMATION PROCESSING LETTERS 1984年第3期18卷 123-128页

作者： ZEMEL, E J.L. Kellogg Graduate School of Management Northwestern University Evanston IL 60201 U.S.A.

An O(n) algorithm for the linear Multiple Choice Knapsack Problem and its d-dimensional generalization are presented, based on Megiddo's (1982) algorithm for linear programming. A certain type of convex programming problem which is common in geometric location models is also considered. An application of the linear case is an O(n) algorithm for locating a least distance hyperplane in R to the d power, according to the rectilinear norm. Previously, the best algorithm available for this problem was an O(n log squared n) algorithm for the 2-dimensional case. A simple application of the nonlinear case is an O(n) algorithm for locating the point at which a ''pursuer'' minimizes its distance from the furthest among n ''targets,'' when the trajectories involved are straight lines in R to the d power.

关键词： linear programming multiple choice knapsack linear algorithms least distance hyperplane

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On sets of linear forms of maximal complexity

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COMPUTATIONAL COMPLEXITY 2023年第1期32卷 1-26页

作者： Kaminski, Michael Shparlinski, Igor E. Waldschmidt, Michel Technion Israel Inst Technol Dept Comp Sci IL-3200003 Haifa Israel Univ New South Wales Sch Math & Stat Sydney NSW 2052 Australia Sorbonne Univ CNRS IMJ PRG F-75005 Paris France Univ Paris CNRS IMJ PRG F-75005 Paris France

We present a uniform description of sets of m linear forms in n variables over the field of rational numbers whose computation requires m(n - 1) additions.

关键词： linear algorithms additive complexity effective Perron theorem common nonzeros of polynomials

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The Test Equation Method for linear State Estimation Based on PMU Data

The Test Equation Method for Linear State Estimation Based o...

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2014 Power Systems Computation Conference (PSCC)

作者： Kolosok, Irina Korkina, Elena Buchinsky, Evgeny Energy Syst Inst SB RAS Irkutsk Russia

ISBN: (纸本)9788393580132

The advent of next generation devices for synchronized phasor measurements (voltage and current values in lines) -PMU- makes it possible to realize linear algorithms of state estimation. The paper suggests the development of the test equation technique for linear state estimation of power system facilities that are monitored on the basis of PMU measurements. New algorithms for the construction of the test equations on the basis of PMU measurements are presented. The algorithms are based on the exclusion of unmeasured variables or state vector components from the electrical circuit equations written in the rectangular coordinates. By virtue of linear nature of these equations the obtained test equations are also linear. The paper presents the algorithms for bad data detection in PMU measurements as well as the algorithms for calculation of estimates, using linear test equations which make it possible to obtain a solution within one iteration. Performance of the algorithms was tested on a test network equipped with PMUs. The developed algorithms allow us to make local state estimation of individual power system facilities (power plants, substations, network sections) that are monitored online on the basis of PMU measurements

关键词： state estimation PMU measurements test equation technique linear algorithms

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Sets of linear Forms Which Are Hard to Compute 46

Sets of Linear Forms Which Are Hard to Compute

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46th International Symposium on Mathematical Foundations of Computer Science, MFCS 2021

作者： Kaminski, Michael Shparlinski, Igor E. Department of Computer Science Technion - Israel Institute of Technology Haifa Israel School of Mathematics and Statistics University of New South Wales Sydney Australia

ISBN: (纸本)9783959772013

We present a uniform description of sets of m linear forms in n variables over the field of rational numbers whose computation requires m(n1) additions. Our result is based on bounds on the height of the annihilating polynomials in the Perron theorem and an effective form of the Lindemann-Weierstrass theorem which is due to Sert (1999). © Michael Kaminski and Igor E. Shparlinski;licensed under Creative Commons License CC-BY 4.0 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021).

关键词： Additive complexity Effective lindemann-weierstrass theorem Effective perron theorem linear algorithms

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Fast and accurate algorithms for projective multi-image structure from motion

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IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE 2001年第6期23卷 546-559页

作者： Oliensis, J Genc, Y NEC Res Inst Princeton NJ 08540 USA Siemens Res Princeton NJ 08540 USA

We describe algorithms for computing projective structure and motion from a multi-image sequence of tracked points. The algorithms are essentially linear, work for any motion of moderate size, and give accuracies similar to those of a maximum-likelihood estimate. They give better results than the Sturm/Triggs factorization approach and are equally fast and they are much faster than bundle adjustment. Our experiments show that the (iterated) Sturm/Triggs approach often fails for linear camera motions. In addition, we study experimentally the common situation where the calibration is fixed and approximately known, comparing the projective versions of our algorithms to mixed projective/Euclidean strategies. We clarify the nature of dominant-plane compensation, showing that it can be considered a small-translation approximation rather than an approximation that the scene is planar. We show that projective algorithms accurately recover the (projected) inverse depths and homographies despite the possibility of transforming the structure and motion by a projective transformation.

关键词： projective multiframe structure from motion structure from motion projective geometry factorization linear algorithms Sturm/Triggs factorization dominant plane bundle adjustment shape from X low level vision

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A convex analytic approach to system identification

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2005年第10期50卷 1550-1566页

作者： Saligrama, V Boston Univ Dept Elect & Comp Engn Boston MA 02215 USA

This paper introduces a new concept for system identification in order to account for random and nonrandom(deterministic/set-membership) uncertainties. While, random/stochastic models are natural for modeling measurement errors, nonrandom uncertainties are well-suited for modeling parametric and nonparametric components. The new concept introduced is distinct from earlier concepts in many respects. First, inspired by the concept of uniform convergence of empirical means developed in machine learning theory, we seek a stronger notion of convergence in that the objective is to obtain probabilistic uniform convergence of model estimates to the minimum possible radius of uncertainty. Second, the formulation lends itself to convex analysis leading to description of optimal algorithms, which turn out to be well-known instrument-variable methods for many of the problems. Third, we characterize conditions on inputs in terms of second-order sample path properties required to achieve the minimum radius of uncertainty. Finally, we present fundamental bounds and optimal algorithms for system identification for a wide variety of standard as well as nonstandard problems that include special structures such as unmodeled dynamics, positive real conditions, bounded sets and linear fractional maps.

关键词： complex systems convex analysis input design linear algorithms robust identification

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Combination of LEDs and cognitive modeling to quantify sheep cheese whey in watercourses

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TALANTA 2019年 203卷 290-296页

作者： Lastra-Mejias, Miguel Villa-Martinez, Alberto Izquierdo, Manuel Aroca-Santos, Regina Cancilla, John C. Torrecilla, Jose S. Univ Complutense Madrid Dept Ingn Quim & Mat E-28040 Madrid Spain Scintillon Inst San Diego CA USA

The concentration of sheep cheese whey (CW) in water obtained from two Spanish reservoirs, two Spanish rivers, and distilled water has been estimated by combining spectroscopic measurements, obtained with light-emitting diodes (LEDs), and linear or non-linear algorithms. The concentration range of CW that has been studied covers from 0 to 25% in weight. Every sample was measured by six different types of LEDs possessing different emission wavelengths (blue, orange, green, pink, white, and UV). 1,800 fluorescence measurements were carried out and used to design different types of models to estimate the concentration of CW in water. The fluorescence spectra provided by the pink LED originated the most accurate mathematical models, with mean square errors lower than 3.3% and 2.5% for the linear and non-linear approaches, respectively. The pink LED combined with the non-linear model, which was an artificial neural network, was further validated through a k-fold cross-validation and an internal validation. It should be noted that the sensor used here has been designed and produced by a 3D printer and has the potential of being implemented in situ for real-time and cost-effective analysis of natural watercourses.

关键词： Artificial neural network Fluorescence Sheep cheese whey linear algorithms Water quality

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An algorithm for partial Grundy number on trees

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DISCRETE MATHEMATICS 2005年第1-3期304卷 108-116页

作者： Shi, Z Goddard, W Hedetniemi, ST Kennedy, K Laskar, R McRae, A Clemson Univ Dept Comp Sci Clemson SC 29634 USA Clemson Univ Dept Math Clemson SC 29634 USA Appalachian State Univ Dept Comp Sci Boone NC 28607 USA

A coloring of a graph G = (V, E) is a partition {V-1, V-2,..., V-k} of V into independent sets or color classes. A vertex v E Vi is a Grundy vertex if it is adjacent to at least one vertex in each color class V-j for every j < i. A coloring is a partial Grundy coloring if every color class contains at least one Grundy vertex, and the partial Grundy number of a graph is the maximum number of colors in a partial Grundy coloring. We derive a natural upper bound on this parameter and show that graphs with sufficiently large girth achieve equality in the bound. In particular, this gives a linear-time algorithm to determine the partial Grundy number of a tree. (c) 2005 Elsevier B.V. All rights reserved.

关键词： partial Grundy coloring linear algorithms graph algorithms tree

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P-4-laden graphs: A new class of brittle graphs

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INFORMATION PROCESSING LETTERS 1996年第1期60卷 29-36页

作者： Giakoumakis, V La.R.I.A. 5 rue du Moulin Neuf (C.U.R.I) Universit&eacute d'Amiens 800OO Amiens France

We present a new family of graphs, the family of P-4-laden graphs strictly containing the class of P-4-lite graphs introduced in (Jamison and Olariu, 1989). We first show that P-4-laden graphs are brittle and next, using modular decomposition we present for this class of graphs a linear recognition algorithm as well as linear algorithms for classical optimization problems.

关键词： brittle graph modular decomposition algorithms linear algorithms

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Considerations on Parallelizing Non-negative Matrix Factorization for Hyperspectral Data Unmixing

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IEEE GEOSCIENCE AND REMOTE SENSING LETTERS 2009年第1期6卷 57-61页

作者： Robila, Stefan A. Maciak, Lukasz G. Montclair State Univ Dept Comp Sci Montclair NJ 07043 USA

Nonnegative matrix factorization (NMF) is a recently developed linear unmixing technique that assumes that the original sources and transform were positively defined. Given that the linear mixing model (LMM) for hyperspectral data requires positive endmembers and abundances, with only minor modifications, NMF can be used to solve LMM. Traditionally, NMF solutions include an iterative process resulting in considerable execution times. In this letter, we provide two novel algorithms aimed at speeding the NW through parallel processing: the first based on the traditional multiplicative solution and the second modifying an adaptive projected gradient technique known to provide better convergence. The algorithms' implementations were tested on various data sets;the results suggest that a significant speedup can be achieved without decrease in accuracy. This supports the further use of NMF for linear unmixing.

关键词： Hyperspectral data linear algorithms linear unmixing nonnegative matrix factorization (NMF) parallel processing remote sensing

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