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This textbook provides concise coverage of the basics of linear and
integer programming which, with megatrends toward optimization,
machine learning, big data, etc., are becoming fundamental toolkits
for data and information science and technology. The authors'
approach is accessible to students from almost all fields of
engineering, including operations research, statistics, machine
learning, control system design, scheduling, formal verification
and computer vision. The presentations enables the basis for
numerous approaches to solving hard combinatorial optimization
problems through randomization and approximation. Readers will
learn to cast various problems that may arise in their research as
optimization problems, understand the cases where the optimization
problem will be linear, choose appropriate solution methods and
interpret results appropriately.
This textbook provides concise coverage of the basics of linear and
integer programming which, with megatrends toward optimization,
machine learning, big data, etc., are becoming fundamental toolkits
for data and information science and technology. The authors'
approach is accessible to students from almost all fields of
engineering, including operations research, statistics, machine
learning, control system design, scheduling, formal verification
and computer vision. The presentations enables the basis for
numerous approaches to solving hard combinatorial optimization
problems through randomization and approximation. Readers will
learn to cast various problems that may arise in their research as
optimization problems, understand the cases where the optimization
problem will be linear, choose appropriate solution methods and
interpret results appropriately.
Design and optimization of integrated circuits are essential to the
creation of new semiconductor chips, and physical optimizations are
becoming more prominent as a result of semiconductor scaling.
Modern chip design has become so complex that it is largely
performed by specialized software, which is frequently updated to
address advances in semiconductor technologies and increased
problem complexities. A user of such software needs a high-level
understanding of the underlying mathematical models and algorithms.
On the other hand, a developer of such software must have a keen
understanding of computer science aspects, including algorithmic
performance bottlenecks and how various algorithms operate and
interact. "VLSI Physical Design: From Graph Partitioning to Timing
Closure" introduces and compares algorithms that are used during
the physical design phase of integrated-circuit design, wherein a
geometric chip layout is produced starting from an abstract circuit
design. The emphasis is on essential and fundamental techniques,
ranging from hypergraph partitioning and circuit placement to
timing closure.
The complexity of modern chip design requires extensive use of
specialized software throughout the process. To achieve the
best results, a user of this software needs a high-level
understanding of the underlying mathematical models and algorithms.
In addition, a developer of such software must have a keen
understanding of relevant computer science aspects, including
algorithmic performance bottlenecks and how
various algorithms operate and interact. This book introduces
and compares the fundamental algorithms that are used during
the IC physical design phase, wherein a geometric chip layout
is produced starting from an abstract circuit design. This updated
second edition includes recent advancements in the
state-of-the-art of physical design, and builds upon
foundational coverage of essential and fundamental techniques.
Numerous examples and tasks with solutions increase the
clarity of presentation and facilitate deeper understanding.
A comprehensive set of slides is available on the Internet
for each chapter, simplifying use of the book in
instructional settings. “This improved, second edition of the
book will continue to serve the EDA and design community
well. It is a foundational text and reference for the next
generation of professionals who will be called on to continue
the advancement of our chip design tools and design the most
advanced micro-electronics.” Dr. Leon Stok, Vice
President, Electronic Design Automation, IBM Systems Group “This
is the book I wish I had when I taught EDA in the past, and the one
I’m using from now on.” Dr. Louis K. Scheffer,
Howard Hughes Medical Institute “I would happily use this book
when teaching Physical Design. I know of no other
work that’s as comprehensive and up-to-date, with
algorithmic focus and clear pseudocode for the key
algorithms. The book is beautifully designed!” Prof. John P.
Hayes, University of Michigan “The entire field of electronic
design automation owes the authors a great debt for
providing a single coherent source on physical design that is
clear and tutorial in nature, while providing details on key
state-of-the-art topics such as timing closure.” Prof. Kurt
Keutzer, University of California, Berkeley “An excellent balance
of the basics and more advanced concepts, presented by top
experts in the field.” Prof. Sachin Sapatnekar, University
of Minnesota
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.
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.
The complexity of modern chip design requires extensive use of
specialized software throughout the process. To achieve the best
results, a user of this software needs a high-level understanding
of the underlying mathematical models and algorithms. In addition,
a developer of such software must have a keen understanding of
relevant computer science aspects, including algorithmic
performance bottlenecks and how various algorithms operate and
interact. This book introduces and compares the fundamental
algorithms that are used during the IC physical design phase,
wherein a geometric chip layout is produced starting from an
abstract circuit design. This updated second edition includes
recent advancements in the state-of-the-art of physical design, and
builds upon foundational coverage of essential and fundamental
techniques. Numerous examples and tasks with solutions increase the
clarity of presentation and facilitate deeper understanding. A
comprehensive set of slides is available on the Internet for each
chapter, simplifying use of the book in instructional settings.
"This improved, second edition of the book will continue to serve
the EDA and design community well. It is a foundational text and
reference for the next generation of professionals who will be
called on to continue the advancement of our chip design tools and
design the most advanced micro-electronics." Dr. Leon Stok, Vice
President, Electronic Design Automation, IBM Systems Group "This is
the book I wish I had when I taught EDA in the past, and the one
I'm using from now on." Dr. Louis K. Scheffer, Howard Hughes
Medical Institute "I would happily use this book when teaching
Physical Design. I know of no other work that's as comprehensive
and up-to-date, with algorithmic focus and clear pseudocode for the
key algorithms. The book is beautifully designed!" Prof. John P.
Hayes, University of Michigan "The entire field of electronic
design automation owes the authors a great debt for providing a
single coherent source on physical design that is clear and
tutorial in nature, while providing details on key state-of-the-art
topics such as timing closure." Prof. Kurt Keutzer, University of
California, Berkeley "An excellent balance of the basics and more
advanced concepts, presented by top experts in the field." Prof.
Sachin Sapatnekar, University of Minnesota
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