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The field of parameterized complexity/multivariate complexity algorithmics is an exciting and vibrant part of theoretical computer science, responding to the vital need for efficient algorithms in modern society. This comprehensive and self-contained textbook presents an accessible overview of the state of the art of multivariate algorithmics and complexity. Increasingly, multivariate algorithmics is having significant practical impact in many application domains, with even more developments on the horizon. The text describes how the multivariate framework allows an extended dialog with a problem, enabling the reader who masters the complexity issues under discussion to use the positive and negative toolkits in their own research. Topics and features: Describes many of the standard algorithmic techniques available for establishing parametric tractability Reviews the classical hardness classes Explores the various limitations and relaxations of the methods Showcases the powerful new lower bound techniques Examines various different algorithmic solutions to the same problems, highlighting the insights to be gained from each approach Demonstrates how complexity methods and ideas have evolved over the past 25 years This classroom-tested and easy-to-follow textbook/reference is essential reading for the beginning graduate student and advanced undergraduate student. The book will also serve as an invaluable resource for the general computer scientist and the mathematically-aware scientist seeking tools for their research.

Engineering & Applied Sciences --- Computer Science --- Computer science. --- Algorithms. --- Computer Science. --- Algorithm Analysis and Problem Complexity. --- Mathematics of Algorithmic Complexity. --- Algorism --- Algebra --- Arithmetic --- Informatics --- Science --- Foundations --- Computer software. --- Software, Computer --- Computer systems --- Computer algorithms. --- Computer science --- Mathematics.

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This Festschrift is in honor of Ker-I Ko, Professor in the Stony Brook University, USA. Ker-I Ko was one of the founding fathers of computational complexity over real numbers and analysis. He and Harvey Friedman devised a theoretical model for real number computations by extending the computation of Turing machines. He contributed significantly to advancing the theory of structural complexity, especially on polynomial-time isomorphism, instance complexity, and relativization of polynomial-time hierarchy. Ker-I also made many contributions to approximation algorithm theory of combinatorial optimization problems. This volume contains 17 contributions in the area of complexity and approximation. Those articles are authored by researchers over the world, including North America, Europe and Asia. Most of them are co-authors, colleagues, friends, and students of Ker-I Ko.

Algorithms. --- Algorithm Analysis and Problem Complexity. --- Mathematics of Algorithmic Complexity. --- Algorism --- Algebra --- Arithmetic --- Foundations --- Computational complexity. --- Complexity, Computational --- Electronic data processing --- Machine theory --- Mathematics. --- Applications of Mathematics. --- Math --- Science

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The present volume contains invited talks of 11th biennial conference on “Emerging Mathematical Methods, Models and Algorithms for Science and Technology”. The main message of the book is that mathematics has a great potential to analyse and understand the challenging problems of nanotechnology, biotechnology, medical science, oil industry and financial technology. The book highlights all the features and main theme discussed in the conference. All contributing authors are eminent academicians, scientists, researchers and scholars in their respective fields, hailing from around the world.

Applied Mathematics --- Engineering & Applied Sciences --- Mathematical models --- Models, Mathematical --- Mathematics. --- Algorithms. --- Mathematical models. --- Geometry. --- Mathematical optimization. --- Mathematical Modeling and Industrial Mathematics. --- Mathematics of Algorithmic Complexity. --- Optimization. --- Simulation methods --- Mathematics --- Euclid's Elements --- Algorism --- Algebra --- Arithmetic --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- System analysis --- Foundations

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This thesis presents an accurate and advanced numerical methodology to remedy difficulties such as direct numerical simulation of magnetohydrodynamic (MHD) flow in computational fluid dynamics (CFD), grid generation processes in tokamak fusion facilities, and the coupling between the surface tension force and Lorentz force in the metallurgical industry. In addition, on the basis of the numerical platform it establishes, it also investigates selected interesting topics, e.g. single bubble motion under the influence of either vertical or horizontal magnetic fields. Furthermore, it confirms the relation between the bubble’s path instability and wake instability, and observes the anisotropic (isotropic) effect of the vertical (horizontal) magnetic field on the vortex structures, which determines the dynamic behavior of the rising bubble. The direct numerical simulation of magnetohydrodynamic (MHD) flows has proven difficult in the field of computational fluid dynamic (CFD) research, because it not only concerns the coupling of the equations governing the electromagnetic field and the fluid motion, but also calls for suitable numerical methods for computing the electromagnetic field. In tokamak fusion facilities, where the MHD effect is significant and the flow domain is complex, the process of grid generation requires considerable time and effort. Moreover, in the metallurgical industry, where multiphase MHD flows are usually encountered, the coupling between the surface tension force and Lorentz force adds to the difficulty of deriving direct numerical simulations.

Magnetohydrodynamics --- Mathematical models. --- Hydraulic engineering. --- Mechanics. --- Engineering Fluid Dynamics. --- Classical Mechanics. --- Mathematics of Algorithmic Complexity. --- Classical mechanics --- Newtonian mechanics --- Physics --- Dynamics --- Quantum theory --- Engineering, Hydraulic --- Engineering --- Fluid mechanics --- Hydraulics --- Shore protection --- Fluid mechanics. --- Algorithms. --- Algorism --- Algebra --- Arithmetic --- Hydromechanics --- Continuum mechanics --- Foundations

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Michael Holzhauser discusses generalizations of well-known network flow and packing problems by additional or modified side constraints. By exploiting the inherent connection between the two problem classes, the author investigates the complexity and approximability of several novel network flow and packing problems and presents combinatorial solution and approximation algorithms. Contents Fractional Packing and Parametric Search Frameworks Budget-Constrained Minimum Cost Flows: The Continuous Case Budget-Constrained Minimum Cost Flows: The Discrete Case Generalized Processing Networks Convex Generalized Flows Target Groups Researchers and students in the fields of mathematics, computer science, and economics Practitioners in operations research and logistics The Author Dr. Michael Holzhauser studied computer science at the University of Kaiserslautern and is now a research fellow in the Optimization Research Group at the Department of Mathematics of the University of Kaiserslautern.

Numerical methods of optimisation --- Operational research. Game theory --- Discrete mathematics --- Mathematics --- Computer science --- discrete wiskunde --- wiskunde --- algoritmen --- Algorithms. --- Discrete Optimization. --- Mathematics of Algorithmic Complexity. --- Algorism --- Algebra --- Arithmetic --- Foundations --- Mathematical optimization. --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis