Linus Schrage

Bio: Linus Schrage is an academic researcher from University of Chicago. The author has contributed to research in topics: Branch and bound & Integer programming. The author has an hindex of 31, co-authored 59 publications receiving 7302 citations. Previous affiliations of Linus Schrage include Université catholique de Louvain & Oklahoma State University–Stillwater.

A Guide to Simulation.

Abstract: Bratley, Fox, and Schrage’s A Guide to Simulation provides practical recommendations for both the novice and the experienced simulationist, without insulting the reader’s intelligence. It does this with a text that is readable, mathematically precise, and comprehensive enough so that it touches on the majority of concerns which arise in a simulation project. Despite the brevity of the book (only 287 pages of text), its mathematical notation, and the problems which it poses without solutions, the textbook is imbued with a feeling for the &dquo;nitty-gritty&dquo; practical aspects of simulation. The authors generously present many helpful hints, suggestions, recommendations, and caveats gleaned from practical experience.

Application of the Branch and Bound Technique to Some Flow-Shop Scheduling Problems

Abstract: The branch-and-bound technique of Little, et al. and Land and Doig is presented and then applied to two flow-shop scheduling problems. Computational results for up to 9 jobs are given for the 2-machine problem when the objective is minimizing the mean completion time. This problem was previously untreated. Results for up to 10 jobs, including comparisons with other techniques, are given for the 3-machine problem when the objective is minimizing the makespan.

Numerical Recipes in C: The Art of Scientific Computing

Abstract: From the Publisher: This is the revised and greatly expanded Second Edition of the hugely popular Numerical Recipes: The Art of Scientific Computing. The product of a unique collaboration among four leading scientists in academic research and industry, Numerical Recipes is a complete text and reference book on scientific computing. In a self-contained manner it proceeds from mathematical and theoretical considerations to actual practical computer routines. With over 100 new routines (now well over 300 in all), plus upgraded versions of many of the original routines, this book is more than ever the most practical, comprehensive handbook of scientific computing available today. The book retains the informal, easy-to-read style that made the first edition so popular, with many new topics presented at the same accessible level. In addition, some sections of more advanced material have been introduced, set off in small type from the main body of the text. Numerical Recipes is an ideal textbook for scientists and engineers and an indispensable reference for anyone who works in scientific computing. Highlights of the new material include a new chapter on integral equations and inverse methods; multigrid methods for solving partial differential equations; improved random number routines; wavelet transforms; the statistical bootstrap method; a new chapter on "less-numerical" algorithms including compression coding and arbitrary precision arithmetic; band diagonal linear systems; linear algebra on sparse matrices; Cholesky and QR decomposition; calculation of numerical derivatives; Pade approximants, and rational Chebyshev approximation; new special functions; Monte Carlo integration in high-dimensional spaces; globally convergent methods for sets of nonlinear equations; an expanded chapter on fast Fourier methods; spectral analysis on unevenly sampled data; Savitzky-Golay smoothing filters; and two-dimensional Kolmogorov-Smirnoff tests. All this is in addition to material on such basic top

Optimization and Approximation in Deterministic Sequencing and Scheduling: a Survey

Abstract: The theory of deterministic sequencing and scheduling has expanded rapidly during the past years. In this paper we survey the state of the art with respect to optimization and approximation algorithms and interpret these in terms of computational complexity theory. Special cases considered are single machine scheduling, identical, uniform and unrelated parallel machine scheduling, and open shop, flow shop and job shop scheduling. We indicate some problems for future research and include a selective bibliography.

Markov Chains for Exploring Posterior Distributions

Abstract: Several Markov chain methods are available for sampling from a posterior distribution. Two important examples are the Gibbs sampler and the Metropolis algorithm. In addition, several strategies are available for constructing hybrid algorithms. This paper outlines some of the basic methods and strategies and discusses some related theoretical and practical issues. On the theoretical side, results from the theory of general state space Markov chains can be used to obtain convergence rates, laws of large numbers and central limit theorems for estimates obtained from Markov chain methods. These theoretical results can be used to guide the construction of more efficient algorithms. For the practical use of Markov chain methods, standard simulation methodology provides several variance reduction techniques and also give guidance on the choice of sample size and allocation.

Bayesian analysis of binary and polychotomous response data

Abstract: A vast literature in statistics, biometrics, and econometrics is concerned with the analysis of binary and polychotomous response data. The classical approach fits a categorical response regression model using maximum likelihood, and inferences about the model are based on the associated asymptotic theory. The accuracy of classical confidence statements is questionable for small sample sizes. In this article, exact Bayesian methods for modeling categorical response data are developed using the idea of data augmentation. The general approach can be summarized as follows. The probit regression model for binary outcomes is seen to have an underlying normal regression structure on latent continuous data. Values of the latent data can be simulated from suitable truncated normal distributions. If the latent data are known, then the posterior distribution of the parameters can be computed using standard results for normal linear models. Draws from this posterior are used to sample new latent data, and t...

Principles and Practices of Interconnection Networks

Abstract: One of the greatest challenges faced by designers of digital systems is optimizing the communication and interconnection between system components. Interconnection networks offer an attractive and economical solution to this communication crisis and are fast becoming pervasive in digital systems. Current trends suggest that this communication bottleneck will be even more problematic when designing future generations of machines. Consequently, the anatomy of an interconnection network router and science of interconnection network design will only grow in importance in the coming years. This book offers a detailed and comprehensive presentation of the basic principles of interconnection network design, clearly illustrating them with numerous examples, chapter exercises, and case studies. It incorporates hardware-level descriptions of concepts, allowing a designer to see all the steps of the process from abstract design to concrete implementation. ·Case studies throughout the book draw on extensive author experience in designing interconnection networks over a period of more than twenty years, providing real world examples of what works, and what doesn't. ·Tightly couples concepts with implementation costs to facilitate a deeper understanding of the tradeoffs in the design of a practical network. ·A set of examples and exercises in every chapter help the reader to fully understand all the implications of every design decision. Table of Contents Chapter 1 Introduction to Interconnection Networks 1.1 Three Questions About Interconnection Networks 1.2 Uses of Interconnection Networks 1.3 Network Basics 1.4 History 1.5 Organization of this Book Chapter 2 A Simple Interconnection Network 2.1 Network Specifications and Constraints 2.2 Topology 2.3 Routing 2.4 Flow Control 2.5 Router Design 2.6 Performance Analysis 2.7 Exercises Chapter 3 Topology Basics 3.1 Nomenclature 3.2 Traffic Patterns 3.3 Performance 3.4 Packaging Cost 3.5 Case Study: The SGI Origin 2000 3.6 Bibliographic Notes 3.7 Exercises Chapter 4 Butterfly Networks 4.1 The Structure of Butterfly Networks 4.2 Isomorphic Butterflies 4.3 Performance and Packaging Cost 4.4 Path Diversity and Extra Stages 4.5 Case Study: The BBN Butterfly 4.6 Bibliographic Notes 4.7 Exercises Chapter 5 Torus Networks 5.1 The Structure of Torus Networks 5.2 Performance 5.3 Building Mesh and Torus Networks 5.4 Express Cubes 5.5 Case Study: The MIT J-Machine 5.6 Bibliographic Notes 5.7 Exercises Chapter 6 Non-Blocking Networks 6.1 Non-Blocking vs. Non-Interfering Networks 6.2 Crossbar Networks 6.3 Clos Networks 6.4 Benes Networks 6.5 Sorting Networks 6.6 Case Study: The Velio VC2002 (Zeus) Grooming Switch 6.7 Bibliographic Notes 6.8 Exercises Chapter 7 Slicing and Dicing 7.1 Concentrators and Distributors 7.2 Slicing and Dicing 7.3 Slicing Multistage Networks 7.4 Case Study: Bit Slicing in the Tiny Tera 7.5 Bibliographic Notes 7.6 Exercises Chapter 8 Routing Basics 8.1 A Routing Example 8.2 Taxonomy of Routing Algorithms 8.3 The Routing Relation 8.4 Deterministic Routing 8.5 Case Study: Dimension-Order Routing in the Cray T3D 8.6 Bibliographic Notes 8.7 Exercises Chapter 9 Oblivious Routing 9.1 Valiant's Randomized Routing Algorithm 9.2 Minimal Oblivious Routing 9.3 Load-Balanced Oblivious Routing 9.4 Analysis of Oblivious Routing 9.5 Case Study: Oblivious Routing in the Avici Terabit Switch Router(TSR) 9.6 Bibliographic Notes 9.7 Exercises Chapter 10 Adaptive Routing 10.1 Adaptive Routing Basics 10.2 Minimal Adaptive Routing 10.3 Fully Adaptive Routing 10.4 Load-Balanced Adaptive Routing 10.5 Search-Based Routing 10.6 Case Study: Adaptive Routing in the Thinking Machines CM-5 10.7 Bibliographic Notes 10.8 Exercises Chapter 11 Routing Mechanics 11.1 Table-Based Routing 11.2 Algorithmic Routing 11.3 Case Study: Oblivious Source Routing in the IBM Vulcan Network 11.4 Bibliographic Notes 11.5 Exercises Chapter 12 Flow Control Basics 12.1 Resources and Allocation Units 12.2 Bufferless Flow Control 12.3 Circuit Switching 12.4 Bibliographic Notes 12.5 Exercises Chapter 13 Buffered Flow Control 13.1 Packet-Buffer Flow Control 13.2 Flit-Buffer Flow Control 13.3 Buffer Management and Backpressure 13.4 Flit-Reservation Flow Control 13.5 Bibliographic Notes 13.6 Exercises Chapter 14 Deadlock and Livelock 14.1 Deadlock 14.2 Deadlock Avoidance 14.3 Adaptive Routing 14.4 Deadlock Recovery 14.5 Livelock 14.6 Case Study: Deadlock Avoidance in the Cray T3E 14.7 Bibliographic Notes 14.8 Exercises Chapter 15 Quality of Service 15.1 Service Classes and Service Contracts 15.2 Burstiness and Network Delays 15.3 Implementation of Guaranteed Services 15.4 Implementation of Best-Effort Services 15.5 Separation of Resources 15.6 Case Study: ATM Service Classes 15.7 Case Study: Virtual Networks in the Avici TSR 15.8 Bibliographic Notes 15.9 Exercises Chapter 16 Router Architecture 16.1 Basic Router Architecture 16.2 Stalls 16.3 Closing the Loop with Credits 16.4 Reallocating a Channel 16.5 Speculation and Lookahead 16.6 Flit and Credit Encoding 16.7 Case Study: The Alpha 21364 Router 16.8 Bibliographic Notes 16.9 Exercises Chapter 17 Router Datapath Components 17.1 Input Buffer Organization 17.2 Switches 17.3 Output Organization 17.4 Case Study: The Datapath of the IBM Colony Router 17.5 Bibliographic Notes 17.6 Exercises Chapter 18 Arbitration 18.1 Arbitration Timing 18.2 Fairness 18.3 Fixed Priority Arbiter 18.4 Variable Priority Iterative Arbiters 18.5 Matrix Arbiter 18.6 Queuing Arbiter 18.7 Exercises Chapter 19 Allocation 19.1 Representations 19.2 Exact Algorithms 19.3 Separable Allocators 19.4 Wavefront Allocator 19.5 Incremental vs. Batch Allocation 19.6 Multistage Allocation 19.7 Performance of Allocators 19.8 Case Study: The Tiny Tera Allocator 19.9 Bibliographic Notes 19.10 Exercises Chapter 20 Network Interfaces 20.1 Processor-Network Interface 20.2 Shared-Memory Interface 20.3 Line-Fabric Interface 20.4 Case Study: The MIT M-Machine Network Interface 20.5 Bibliographic Notes 20.6 Exercises Chapter 21 Error Control 411 21.1 Know Thy Enemy: Failure Modes and Fault Models 21.2 The Error Control Process: Detection, Containment, and Recovery 21.3 Link Level Error Control 21.4 Router Error Control 21.5 Network-Level Error Control 21.6 End-to-end Error Control 21.7 Bibliographic Notes 21.8 Exercises Chapter 22 Buses 22.1 Bus Basics 22.2 Bus Arbitration 22.3 High Performance Bus Protocol 22.4 From Buses to Networks 22.5 Case Study: The PCI Bus 22.6 Bibliographic Notes 22.7 Exercises Chapter 23 Performance Analysis 23.1 Measures of Interconnection Network Performance 23.2 Analysis 23.3 Validation 23.4 Case Study: Efficiency and Loss in the BBN Monarch Network 23.5 Bibliographic Notes 23.6 Exercises Chapter 24 Simulation 24.1 Levels of Detail 24.2 Network Workloads 24.3 Simulation Measurements 24.4 Simulator Design 24.5 Bibliographic Notes 24.6 Exercises Chapter 25 Simulation Examples 495 25.1 Routing 25.2 Flow Control Performance 25.3 Fault Tolerance Appendix A Nomenclature Appendix B Glossary Appendix C Network Simulator