Optimal Interconnection Trees in the Plane

Optimal Interconnection Trees in the Plane PDF Author: Marcus Brazil
Publisher: Springer
ISBN: 3319139150
Category : Mathematics
Languages : en
Pages : 344

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Book Description
This book explores fundamental aspects of geometric network optimisation with applications to a variety of real world problems. It presents, for the first time in the literature, a cohesive mathematical framework within which the properties of such optimal interconnection networks can be understood across a wide range of metrics and cost functions. The book makes use of this mathematical theory to develop efficient algorithms for constructing such networks, with an emphasis on exact solutions. Marcus Brazil and Martin Zachariasen focus principally on the geometric structure of optimal interconnection networks, also known as Steiner trees, in the plane. They show readers how an understanding of this structure can lead to practical exact algorithms for constructing such trees. The book also details numerous breakthroughs in this area over the past 20 years, features clearly written proofs, and is supported by 135 colour and 15 black and white figures. It will help graduate students, working mathematicians, engineers and computer scientists to understand the principles required for designing interconnection networks in the plane that are as cost efficient as possible.

Experimental Algorithms

Experimental Algorithms PDF Author: Andrew V. Goldberg
Publisher: Springer
ISBN: 3319388517
Category : Computers
Languages : en
Pages : 386

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Book Description
This book constitutes the refereed proceedings of the 15th International Symposium on Experimental Algorithms, SEA 2016, held in St. Petersburg, Russia, in June 2016. The 25 revised full papers presented were carefully reviewed and selected from 54 submissions. The main theme of the symposium is the role of experimentation and of algorithm engineering techniques in the design and evaluation of algorithms and data structures. SEA covers a wide range of topics in experimental algorithmics, bringing together researchers from algorithm engineering, mathematical programming, and combinatorial optimization communities.

Computing and Combinatorics

Computing and Combinatorics PDF Author: Donghyun Kim
Publisher: Springer Nature
ISBN: 3030581500
Category : Computers
Languages : en
Pages : 678

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Book Description
This book constitutes the proceedings of the 26th International Conference on Computing and Combinatorics, COCOON 2020, held in Atlanta, GA, USA, in August 2020. Due to the COVID-19 pandemic COCOON 2020 was organized as a fully online conference. The 54 papers presented in this volume were carefully reviewed and selected from 126 submissions. The papers cover various topics, including algorithm design, approximation algorithm, graph theory, complexity theory, problem solving, optimization, computational biology, computational learning, communication network, logic, and game theory.

New Trends in Intuitive Geometry

New Trends in Intuitive Geometry PDF Author: Gergely Ambrus
Publisher: Springer
ISBN: 3662574136
Category : Mathematics
Languages : en
Pages : 458

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Book Description
This volume contains 17 surveys that cover many recent developments in Discrete Geometry and related fields. Besides presenting the state-of-the-art of classical research subjects like packing and covering, it also offers an introduction to new topological, algebraic and computational methods in this very active research field. The readers will find a variety of modern topics and many fascinating open problems that may serve as starting points for research.

On Optimal Interconnections for VLSI

On Optimal Interconnections for VLSI PDF Author: Andrew B. Kahng
Publisher: Springer Science & Business Media
ISBN: 1475723636
Category : Technology & Engineering
Languages : en
Pages : 286

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Book Description
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.

Encyclopedia of Optimization

Encyclopedia of Optimization PDF Author: Christodoulos A. Floudas
Publisher: Springer Science & Business Media
ISBN: 0387747583
Category : Mathematics
Languages : en
Pages : 4622

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Book Description
The goal of the Encyclopedia of Optimization is to introduce the reader to a complete set of topics that show the spectrum of research, the richness of ideas, and the breadth of applications that has come from this field. The second edition builds on the success of the former edition with more than 150 completely new entries, designed to ensure that the reference addresses recent areas where optimization theories and techniques have advanced. Particularly heavy attention resulted in health science and transportation, with entries such as "Algorithms for Genomics", "Optimization and Radiotherapy Treatment Design", and "Crew Scheduling".

Steiner Trees in Industry

Steiner Trees in Industry PDF Author: Xiuzhen Cheng
Publisher: Springer Science & Business Media
ISBN: 1461302552
Category : Computers
Languages : en
Pages : 507

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Book Description
This book is a collection of articles studying various Steiner tree prob lems with applications in industries, such as the design of electronic cir cuits, computer networking, telecommunication, and perfect phylogeny. The Steiner tree problem was initiated in the Euclidean plane. Given a set of points in the Euclidean plane, the shortest network interconnect ing the points in the set is called the Steiner minimum tree. The Steiner minimum tree may contain some vertices which are not the given points. Those vertices are called Steiner points while the given points are called terminals. The shortest network for three terminals was first studied by Fermat (1601-1665). Fermat proposed the problem of finding a point to minimize the total distance from it to three terminals in the Euclidean plane. The direct generalization is to find a point to minimize the total distance from it to n terminals, which is still called the Fermat problem today. The Steiner minimum tree problem is an indirect generalization. Schreiber in 1986 found that this generalization (i.e., the Steiner mini mum tree) was first proposed by Gauss.

Optimal Interconnection Trees in the Plane

Optimal Interconnection Trees in the Plane PDF Author: Marcus Brazil
Publisher: Springer
ISBN: 3319139150
Category : Mathematics
Languages : en
Pages : 344

View

Book Description
This book explores fundamental aspects of geometric network optimisation with applications to a variety of real world problems. It presents, for the first time in the literature, a cohesive mathematical framework within which the properties of such optimal interconnection networks can be understood across a wide range of metrics and cost functions. The book makes use of this mathematical theory to develop efficient algorithms for constructing such networks, with an emphasis on exact solutions. Marcus Brazil and Martin Zachariasen focus principally on the geometric structure of optimal interconnection networks, also known as Steiner trees, in the plane. They show readers how an understanding of this structure can lead to practical exact algorithms for constructing such trees. The book also details numerous breakthroughs in this area over the past 20 years, features clearly written proofs, and is supported by 135 colour and 15 black and white figures. It will help graduate students, working mathematicians, engineers and computer scientists to understand the principles required for designing interconnection networks in the plane that are as cost efficient as possible.

Experimental Algorithms

Experimental Algorithms PDF Author: Andrew V. Goldberg
Publisher: Springer
ISBN: 3319388517
Category : Computers
Languages : en
Pages : 386

View

Book Description
This book constitutes the refereed proceedings of the 15th International Symposium on Experimental Algorithms, SEA 2016, held in St. Petersburg, Russia, in June 2016. The 25 revised full papers presented were carefully reviewed and selected from 54 submissions. The main theme of the symposium is the role of experimentation and of algorithm engineering techniques in the design and evaluation of algorithms and data structures. SEA covers a wide range of topics in experimental algorithmics, bringing together researchers from algorithm engineering, mathematical programming, and combinatorial optimization communities.

Computing and Combinatorics

Computing and Combinatorics PDF Author: Donghyun Kim
Publisher: Springer Nature
ISBN: 3030581500
Category : Computers
Languages : en
Pages : 678

View

Book Description
This book constitutes the proceedings of the 26th International Conference on Computing and Combinatorics, COCOON 2020, held in Atlanta, GA, USA, in August 2020. Due to the COVID-19 pandemic COCOON 2020 was organized as a fully online conference. The 54 papers presented in this volume were carefully reviewed and selected from 126 submissions. The papers cover various topics, including algorithm design, approximation algorithm, graph theory, complexity theory, problem solving, optimization, computational biology, computational learning, communication network, logic, and game theory.

New Trends in Intuitive Geometry

New Trends in Intuitive Geometry PDF Author: Gergely Ambrus
Publisher: Springer
ISBN: 3662574136
Category : Mathematics
Languages : en
Pages : 458

View

Book Description
This volume contains 17 surveys that cover many recent developments in Discrete Geometry and related fields. Besides presenting the state-of-the-art of classical research subjects like packing and covering, it also offers an introduction to new topological, algebraic and computational methods in this very active research field. The readers will find a variety of modern topics and many fascinating open problems that may serve as starting points for research.

On Optimal Interconnections for VLSI

On Optimal Interconnections for VLSI PDF Author: Andrew B. Kahng
Publisher: Springer Science & Business Media
ISBN: 1475723636
Category : Technology & Engineering
Languages : en
Pages : 286

View

Book Description
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.

Encyclopedia of Optimization

Encyclopedia of Optimization PDF Author: Christodoulos A. Floudas
Publisher: Springer Science & Business Media
ISBN: 0387747583
Category : Mathematics
Languages : en
Pages : 4622

View

Book Description
The goal of the Encyclopedia of Optimization is to introduce the reader to a complete set of topics that show the spectrum of research, the richness of ideas, and the breadth of applications that has come from this field. The second edition builds on the success of the former edition with more than 150 completely new entries, designed to ensure that the reference addresses recent areas where optimization theories and techniques have advanced. Particularly heavy attention resulted in health science and transportation, with entries such as "Algorithms for Genomics", "Optimization and Radiotherapy Treatment Design", and "Crew Scheduling".

Computer Systems Science & Engineering

Computer Systems Science & Engineering PDF Author:
Publisher:
ISBN:
Category : Computer engineering
Languages : en
Pages :

View

Book Description


Steiner Trees in Industry

Steiner Trees in Industry PDF Author: Xiuzhen Cheng
Publisher: Springer Science & Business Media
ISBN: 1461302552
Category : Computers
Languages : en
Pages : 507

View

Book Description
This book is a collection of articles studying various Steiner tree prob lems with applications in industries, such as the design of electronic cir cuits, computer networking, telecommunication, and perfect phylogeny. The Steiner tree problem was initiated in the Euclidean plane. Given a set of points in the Euclidean plane, the shortest network interconnect ing the points in the set is called the Steiner minimum tree. The Steiner minimum tree may contain some vertices which are not the given points. Those vertices are called Steiner points while the given points are called terminals. The shortest network for three terminals was first studied by Fermat (1601-1665). Fermat proposed the problem of finding a point to minimize the total distance from it to three terminals in the Euclidean plane. The direct generalization is to find a point to minimize the total distance from it to n terminals, which is still called the Fermat problem today. The Steiner minimum tree problem is an indirect generalization. Schreiber in 1986 found that this generalization (i.e., the Steiner mini mum tree) was first proposed by Gauss.

Providing Quality of Service in Heterogeneous Environments

Providing Quality of Service in Heterogeneous Environments PDF Author: Ralf Lehnert, Phuoc Tran-Gia, Joachim Charzinsky
Publisher: Elsevier
ISBN: 9789999903219
Category :
Languages : en
Pages :

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Book Description


Algorithms from P to NP: Design & efficiency

Algorithms from P to NP: Design & efficiency PDF Author: Bernard M. E. Moret
Publisher: Addison-Wesley
ISBN:
Category : Computers
Languages : en
Pages : 576

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Book Description