Minimal Networksthe Steiner Problem And Its Generalizations
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Minimal NetworksThe Steiner Problem and Its Generalizations by Alexander O. Ivanov,Alexei A. Tuzhilin Pdf
This book focuses on the classic Steiner Problem and illustrates how results of the problem's development have generated the Theory of Minimal Networks, that is systems of "rubber" branching threads of minimal length. This theory demonstrates a brilliant interconnection among differential and computational geometry, topology, variational calculus, and graph theory. All necessary preliminary information is included, and the book's simplified format and nearly 150 illustrations and tables will help readers develop a concrete understanding of the material. All nontrivial statements are proved, and plenty of exercises are included.
Steiner Tree Problems in Computer Communication Networks by Dingzhu Du,Xiaodong Hu Pdf
The Steiner tree problem is one of the most important combinatorial optimization problems. It has a long history that can be traced back to the famous mathematician Fermat (1601-1665). This book studies three significant breakthroughs on the Steiner tree problem that were achieved in the 1990s, and some important applications of Steiner tree problems in computer communication networks researched in the past fifteen years. It not only covers some of the most recent developments in Steiner tree problems, but also discusses various combinatorial optimization methods, thus providing a balance between theory and practice. Sample Chapter(s). Chapter 1: Minimax Approach and Steiner Ratio (372 KB). Contents: Minimax Approach and Steiner Ratio; k -Steiner Ratios and Better Approximation Algorithms; Geometric Partitions and Polynomial Time Approximation Schemes; Grade of Service Steiner Tree Problem; Steiner Tree Problem for Minimal Steiner Points; Bottleneck Steiner Tree Problem; Steiner k -Tree and k -Path Routing Problems; Steiner Tree Coloring Problem; Steiner Tree Scheduling Problem; Survivable Steiner Network Problem. Readership: Researchers and graduate students of computer science and engineering as well as operations research.
Branching Solutions To One-dimensional Variational Problems by Alexandr Ivanov,Alexei Avgustinovich Tuzhilin Pdf
This book deals with the new class of one-dimensional variational problems — the problems with branching solutions. Instead of extreme curves (mappings of a segment to a manifold) we investigate extreme networks, which are mappings of graphs (one-dimensional cell complexes) to a manifold. Various applications of the approach are presented, such as several generalizations of the famous Steiner problem of finding the shortest network spanning given points of the plane.
The problem of "Shortest Connectivity", which is discussed here, has a long and convoluted history. Many scientists from many fields as well as laymen have stepped on its stage. Usually, the problem is known as Steiner's Problem and it can be described more precisely in the following way: Given a finite set of points in a metric space, search for a network that connects these points with the shortest possible length. This shortest network must be a tree and is called a Steiner Minimal Tree (SMT). It may contain vertices different from the points which are to be connected. Such points are called Steiner points. Steiner's Problem seems disarmingly simple, but it is rich with possibilities and difficulties, even in the simplest case, the Euclidean plane. This is one of the reasons that an enormous volume of literature has been published, starting in 1 the seventeenth century and continuing until today. The difficulty is that we look for the shortest network overall. Minimum span ning networks have been well-studied and solved eompletely in the case where only the given points must be connected. The novelty of Steiner's Problem is that new points, the Steiner points, may be introduced so that an intercon necting network of all these points will be shorter. This also shows that it is impossible to solve the problem with combinatorial and geometric methods alone.
The aim in this graduate level text is to outline the key mathematical concepts that underpin these important questions in applied mathematics. These concepts involve discrete mathematics (particularly graph theory), optimization, computer science, and several ideas in biology.
Frontiers in Global Optimization by Christodoulos A. Floudas,Panos M. Pardalos Pdf
Global Optimization has emerged as one of the most exciting new areas of mathematical programming. Global optimization has received a wide attraction from many fields in the past few years, due to the success of new algorithms for addressing previously intractable problems from diverse areas such as computational chemistry and biology, biomedicine, structural optimization, computer sciences, operations research, economics, and engineering design and control. This book contains refereed invited papers submitted at the 4th international confer ence on Frontiers in Global Optimization held at Santorini, Greece during June 8-12, 2003. Santorini is one of the few sites of Greece, with wild beauty created by the explosion of a volcano which is in the middle of the gulf of the island. The mystic landscape with its numerous mult-extrema, was an inspiring location particularly for researchers working on global optimization. The three previous conferences on "Recent Advances in Global Opti mization", "State-of-the-Art in Global Optimization", and "Optimization in Computational Chemistry and Molecular Biology: Local and Global approaches" took place at Princeton University in 1991, 1995, and 1999, respectively. The papers in this volume focus on de terministic methods for global optimization, stochastic methods for global optimization, distributed computing methods in global optimization, and applications of global optimiza tion in several branches of applied science and engineering, computer science, computational chemistry, structural biology, and bio-informatics.
Steiner's Problem concerns finding a shortest interconnecting network for a finite set of points in a metric space. A solution must be a tree, which is called a Steiner Minimal Tree (SMT), and may contain vertices different from the points which are to be connected. Steiner's Problem is one of the most famous combinatorial-geometrical problems, but unfortunately it is very difficult in terms of combinatorial structure as well as computational complexity. However, if only a Minimum Spanning Tree (MST) without additional vertices in the interconnecting network is sought, then it is simple to solve. So it is of interest to know what the error is if an MST is constructed instead of an SMT. The worst case for this ratio running over all finite sets is called the Steiner ratio of the space. The book concentrates on investigating the Steiner ratio. The goal is to determine, or at least estimate, the Steiner ratio for many different metric spaces. The author shows that the description of the Steiner ratio contains many questions from geometry, optimization, and graph theory. Audience: Researchers in network design, applied optimization, and design of algorithms.
Models and Algorithms for Global Optimization by Aimo Törn,Julius Žilinskas Pdf
The research of Antanas Zilinskas has focused on developing models for global optimization, implementing and investigating the corresponding algorithms, and applying those algorithms to practical problems. This volume, dedicated to Professor Zilinskas on the occasion of his 60th birthday, contains new survey papers in which leading researchers from the field present various models and algorithms for solving global optimization problems.
Author : José C. Cunha Publisher : Springer Science & Business Media Page : 1311 pages File Size : 43,8 Mb Release : 2005-08-18 Category : Computers ISBN : 9783540287001
Euro-Par 2005 Parallel Processing by José C. Cunha Pdf
Euro-Par 2005 was the eleventh conference in the Euro-Par series. It was organized by the Centre for Informatics and Information Technology (CITI) and the Department of Informatics of the Faculty of Science and Technology of Universidade Nova de Lisboa, at the Campus of Monte de Caparica.
Teaching Secondary Mathematics as if the Planet Matters by Alf Coles,Richard Barwell,Tony Cotton,Jan Winter,Laurinda Brown Pdf
‘This book moves us beyond a theoretical pondering of the issues and makes concrete suggestions for teachers and students for how things can be different in mathematics classrooms. This is long overdue.’ Peter Gates, University of Nottingham Teaching Mathematics as if the Planet Matters explores how Mathematics teachers can develop approaches to curriculum and learning which help students understand the nature of the contemporary world. It sets out a model for teaching and learning that allows teachers to examine existing approaches to teaching and draw upon the insights of mathematics as a discipline to help students relate classroom mathematics to global issues such as climate change, the economy, food supplies, biodiversity, human rights, and social justice. Including practical examples, suggestions for teaching activities and detailed further reading sections, the book covers: the mathematics of description in the measuring, recording and statistical analysis that informs our knowledge of climate change, consumption and sustainability; the mathematics of prediction in the modelling used by governments, scientists and businesses to plan roads, power stations and food supplies and their effects; the mathematics of communication in the news reports, blogs and environmental campaigns, incomplete without graphs, charts and statistics. The true worth of a school subject is revealed in how far it can account for and respond to the major issues of the time. The issue of the environment cuts across subject boundaries and requires an interdisciplinary response. Mathematics teachers are part of that response and they have a crucial role in helping students to respond to environmental issues and representations.
Examining Robustness and Vulnerability of Networked Systems by S. Butenko,E.L. Pasiliao,Volodymyr Shylo,V. Shylo Pdf
Modern critical infrastructure is characterized by complex, heterogeneous and dynamically evolving networks. But these can be vulnerable to component failure, and this is a problem which must be addressed by realistic mathematical models. This book presents papers from the NATO Advanced Research Workshop (ARW), Examining Robustness and Vulnerability of Critical Infrastructure Networks, held in Kiev, Ukraine, in June 2013. Contributions were from workshop participants as well as invited experts in the field, and cover topics including: mathematical models; probability-based risk measures; algorithms for the design and detection of robust structures; identification of critical network components and case studies. This book will be of interest to researchers, practitioners and graduate students in the fields of mathematics, computer science and engineering.
Handbook of Algorithms for Physical Design Automation by Charles J. Alpert,Dinesh P. Mehta,Sachin S. Sapatnekar Pdf
The physical design flow of any project depends upon the size of the design, the technology, the number of designers, the clock frequency, and the time to do the design. As technology advances and design-styles change, physical design flows are constantly reinvented as traditional phases are removed and new ones are added to accommodate changes in
On Optimal Interconnections for VLSI by Andrew B. Kahng,Gabriel Robins Pdf
On Optimal Interconnections for VLSI describes, from a geometric perspective, algorithms for high-performance, high-density interconnections during the global and detailed routing phases of circuit layout. First, the book addresses area minimization, with a focus on near-optimal approximation algorithms for minimum-cost Steiner routing. In addition to practical implementations of recent methods, the implications of recent results on spanning tree degree bounds and the method of Zelikovsky are discussed. Second, the book addresses delay minimization, starting with a discussion of accurate, yet algorithmically tractable, delay models. Recent minimum-delay constructions are highlighted, including provably good cost-radius tradeoffs, critical-sink routing algorithms, Elmore delay-optimal routing, graph Steiner arborescences, non-tree routing, and wiresizing. Third, the book addresses skew minimization for clock routing and prescribed-delay routing formulations. The discussion starts with early matching-based constructions and goes on to treat zero-skew routing with provably minimum wirelength, as well as planar clock routing. Finally, the book concludes with a discussion of multiple (competing) objectives, i.e., how to optimize area, delay, skew, and other objectives simultaneously. These techniques are useful when the routing instance has heterogeneous resources or is highly congested, as in FPGA routing, multi-chip packaging, and very dense layouts. Throughout the book, the emphasis is on practical algorithms and a complete self-contained development. On Optimal Interconnections for VLSI will be of use to both circuit designers (CAD tool users) as well as researchers and developers in the area of performance-driven physical design.
Knowledge-Based Intelligent Information and Engineering Systems by Bogdan Gabrys,Robert J. Howlett Pdf
The three volume set LNAI 4251, LNAI 4252, and LNAI 4253 constitutes the refereed proceedings of the 10th International Conference on Knowledge-Based Intelligent Information and Engineering Systems, KES 2006, held in Bournemouth, UK in October 2006. The 480 revised papers presented were carefully reviewed and selected from about 1400 submissions. The papers present a wealth of original research results from the field of intelligent information processing.