Combinatorial Optimization

By: Jingsheng Jason Cong (Editor), Joseph R. Shinnerl (Editor)

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Hardcover | 31 March 2003

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324 Pages

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24.13 x 16.51 x 1.91

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In the last few decades, multiscale algorithms have become a dominant trend in large-scale scientific computation. Researchers have successfully applied these methods to a wide range of simulation and optimization problems. This book gives a general overview of multiscale algorithms; applications to general combinatorial optimization problems such as graph partitioning and the traveling salesman problem; and VLSICAD applications, including circuit partitioning, placement, and VLSI routing. Additional chapters discuss optimization in reconfigurable computing, convergence in multilevel optimization, and model problems with PDE constraints.

Audience: Written at the graduate level, the book is intended for engineers and mathematical and computational scientists studying large-scale optimization in electronic design automation.

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List of Figures	p. ix
List of Tables	p. xiii
Preface	p. xv
Multigrid Solvers and Multilevel Optimization Strategies	p. 1
Unconstrained quadratic optimization and basic multiscale concepts	p. 4
Linear geometric multigrid	p. 7
Algebraic multigrid (AMG)	p. 13
Numerical homogenization: High-accuracy coarsening	p. 19
Non-symmetric and highly indefinite matrices	p. 21
Non-local equations: Dense matrices	p. 23
Non-quadratic optimization: Nonlinear systems	p. 27
Constrained optimization and eigenproblems	p. 34
Non-deterministic systems	p. 42
Global optimization: Multilevel annealing	p. 49
Graph and hypergraph problems	p. 53
Multilevel formulation	p. 59
An Exploration of Multilevel Combinatorial Optimisation	p. 71
The Graph Partitioning Problem	p. 76
Multilevel graph partitioning	p. 77
Multilevel refinement: experimental results	p. 83
Multilevel landscapes: experimental results	p. 89
Variant problems	p. 96
The Travelling Salesman Problem	p. 97
A multilevel algorithm for the travelling salesman problem	p. 99
Multilevel refinement: experimental results	p. 103
Multilevel landscapes: experimental results	p. 107
Summary	p. 112
A generic multilevel strategy	p. 112
Related work	p. 114
Typical runtime	p. 115
Solution-based coarsening and iterated multilevel algorithms	p. 116
Review of the experimental data	p. 117
Conclusions and future research	p. 118
Multilevel Hypergraph Partitioning	p. 125
Hypergraph Partitioning--Problem Definition	p. 126
Extensions on the Basic Problem	p. 128
Methods for Computing a k-way Partitioning	p. 129
The Multilevel Paradigm for Hypergraph Partitioning	p. 130
The Various Phases of the Multilevel Paradigm	p. 132
Coarsening Phase	p. 132
Initial Partitioning Phase	p. 140
Uncoarsening and Refinement Phase	p. 141
Why Does the Multilevel Paradigm Work?	p. 146
Extensions of the Multilevel Paradigm	p. 148
Direction of Future Research	p. 151
Multilevel Circuit Placement	p. 155
Problem Formulation and Approximations	p. 157
Objective and Constraint Representations	p. 158
Hypergraph and Graph Models	p. 161
Global Placement and Detailed Placement	p. 161
Contemporary Methodology	p. 162
Annealing Methods	p. 162
Analytical Methods	p. 163
Partitioning-Based Methods	p. 165
Hybrid Methods	p. 167
Multilevel Simulated-Annealing-Based Methods	p. 169
mPL: A Multilevel Placement Algorithm	p. 172
Bottom-Up Hierarchy Construction	p. 174
Nonlinear Programming by a Penalized Interior-Point Method	p. 178
Discrete Refinement	p. 184
Numerical Experiments	p. 186
Conclusions	p. 188
Multilevel VLSI Routing	p. 195
Introduction to VLSI Routing Problem	p. 196
Overview of the Routing Flow	p. 200
Coarsening Process and Resource Reservation	p. 202
Merging Resource	p. 204
Resource Reservation	p. 205
Initial Routing	p. 207
History-Based Incremental Refinement	p. 209
The Path Searching Algorithm	p. 210
History-Based Iterative Refinement	p. 211
Experimental Results	p. 213
Optimization for Reconfigurable Systems Using Hierarchical Abstraction	p. 219
Introduction	p. 220
Compilation: Data Communication Minimization	p. 225
Problem Definition	p. 226
Algorithm	p. 229
Customized Resource Allocation	p. 239
Gain and Overlap Model	p. 242
Problem Formulation	p. 244
Overlap Graph	p. 245
Customized Block Selection Algorithm	p. 250
Simultaneous Scheduling and Binding: Customized Resource Utilization/Latency Minimization Trade-off	p. 253
Problem Formulation	p. 253
Proposed Scheduling Algorithm	p. 254
Conclusions	p. 262
Practical Aspects of Multiscale Optimization Methods for VLSICAD	p. 265
The VLSICAD Optimization Model	p. 267
Existing Approaches	p. 269
The Multiscale Optimization Algorithm	p. 272
Properties of the Multiscale Algorithm	p. 274
Practical Issues	p. 281
Computational Examples	p. 285
A Hyperbolic Model Problem	p. 285
An Elliptic Model Problem	p. 288
Conclusions	p. 288
Index	p. 293
Table of Contents provided by Ingram. All Rights Reserved.

Combinatorial Optimization

At a Glance

Hardcover

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