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9781420072730

Introduction to Scheduling

by ;
  • ISBN13:

    9781420072730

  • ISBN10:

    1420072730

  • Edition: 1st
  • Format: Hardcover
  • Copyright: 2009-11-18
  • Publisher: CRC Press

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Summary

Reviewing classical methods as well as realistic models and algorithms, this book offers a through introduction to scheduling presented by highly respected experts. It covers fundamental concepts and basic methods, as well as recent research and applications with a special focus on distributed systems and computational grids, Topics covered include online scheduling, stochastic task-resource systems, and platform models. Though the book takes a rigorous approach, it provides enough background to be self-contained and fully accessible to computer scientists, mathematicians, and researchers in related fields. Examples, theorems, and pedagogical proofs are provided to create an interactive learning format.

Table of Contents

Prefacep. xi
Acknowledgmentsp. xvii
List of.Contributorsp. xix
On the Complexity of Schedulingp. 1
Introductionp. 1
Scheduling Modelsp. 2
Processor (Machine) Schedulingp. 6
Easy and Hard Problemsp. 11
Complexity Classification of Scheduling Problemsp. 18
Referencesp. 20
Approximation Algorithms for Scheduling Problemsp. 23
Introductionp. 23
Approximation Algorithmsp. 24
Definitionsp. 25
Absolute Approximation Algorithms (Case pinf = pSUp)p. 26
A Fully Polynomial-Time Approximation Schemep. 28
Introduction of Precedence Constraintsp. 31
Unbounded Number of Processorsp. 31
Bounded Number of Processorsp. 31
Introduction of Communication Delaysp. 32
Introductionp. 32
Unbounded Number of Processorsp. 33
Limited Number of Processorsp. 37
Introduction of Duplicationp. 42
Large Communication Delaysp. 44
Conclusionp. 47
Referencesp. 48
Online Schedulingp. 51
Introductionp. 51
Classical Scheduling Problemsp. 52
Makespan Minimizationp. 52
Flow Time Objectivesp. 57
Load Balancingp. 60
Energy-Efficient Schedulingp. 62
Power-Down Mechanismsp. 63
Dynamic Speed Scalingp. 67
Conclusionp. 73
Referencesp. 73
Job Schedulingp. 79
Introductionp. 79
Single Machine Problemsp. 82
Makespan Problems on Parallel Machinesp. 86
Completion Time Problems on Parallel Machinesp. 91
Conclusionp. 99
Referencesp. 100
Cyclic Schedulingp. 103
Introductionp. 103
Cyclic Scheduling and Uniform Constraintsp. 104
Common Features of Cyclic Scheduling Problemsp. 104
Uniform Task Systemsp. 106
Questionsp. 108
Periodic Schedules of Uniform Task Systemsp. 109
Properties of Periodic Schedulesp. 109
Critical Circuit of a Strongly Connected Graphp. 112
Computation of an Optimal Periodic Schedulep. 113
Earliest Schedule of Uniform Task Systemsp. 116
Periodic Schedules of Uniform Task Systems with Resource Constraintsp. 117
Which Periodicity?p. 117
Complexity and Iteration Vectorsp. 118
Patterns and Iteration Vectorsp. 119
Decomposed Software Pipelining: A Generic Approachp. 121
Dynamic Schedulesp. 124
Conclusionp. 125
Referencesp. 126
Cyclic Scheduling for the Synthesis of Embedded Systemsp. 129
Introductionp. 129
Problem Formulation and Basic-Notationsp. 131
Synchronous Dataflow Graphsp. 131
Timed Weighted Event Graphsp. 132
Problem Formulationp. 133
Precedence Relations Induced by a Timed Marked WEGp. 134
Characterization of Precedence Relationsp. 134
Timed Event Graphsp. 135
Equivalent Placesp. 135
Unitary WEGsp. 137
Definitionsp. 138
Normalization of a Unitary WEGp. 139
Expansion of a Unitary Timed Marked WEGp. 141
Relationship between Expansion and Normalizationp. 145
Periodic Schedule of a Normalized Timed Marked WEGp. 147
Periodic Schedulesp. 148
Properties of Periodic Schedulesp. 148
Existence of Periodic Schedulesp. 150
Optimal Periodic Schedulep. 152
Conclusionp. 154
Referencesp. 154
Steady-State Schedulingp. 159
Introductionp. 159
Problem Formulationp. 161
Platform Modelp. 161
Applicationsp. 162
Compact Description of a Schedulep. 163
Definition of the Allocationsp. 164
Definition of Valid Patternsp. 166
From Allocations and Valid Patterns to Schedulesp. 167
Conditions and Weak Periodic Schedulesp. 167
Weak Periodic Schedules and Cyclic Schedulingp. 169
Problem Solving in the General Casep. 172
Existence of a Compact Solutionp. 173
Resolution with the Ellipsoid Methodp. 175
Separation in the Dual Linear Programp. 176
Toward Compact Linear Programsp. 178
Introductionp. 178
Efficient Computation of Valid Patterns under the Bidirectional One-Port Modelp. 179
Efficient Computation of Allocationsp. 182
Conclusionp. 184
Referencesp. 185
Divisible Load Schedulingp. 187
Introductionp. 187
Motivating Examplep. 188
Classical Approachp. 188
Divisible Load Approachp. 191
Bus-Shaped Networkp. 192
Star-Shaped Networkp. 195
Extensions of the Divisible Load Modelp. 201
Introducing Latenciesp. 201
Multi-Round Strategiesp. 204
Return Messagesp. 214
Conclusionp. 216
Referencesp. 217
Multi-Objective Schedulingp. 219
Motivationp. 220
Once Upon a Timep. 220
Diversity of Objectivesp. 221
Motivating Problemsp. 222
Summary of Results on Single Objective Problemsp. 223
Beyond the Scope of This, This Chapterp. 223
Chapter Organizationp. 224
What Is Multi-Objective Optimization?p. 225
Overview of the Various Existing Approachesp. 228
Algorithms Building One Trade-off Solutionp. 228
Complexity Issuesp. 230
Zenith Approximation on MaxAndSump. 233
Pareto Set Approximation on EfficientReliablep. 235
Motivationp. 235
Definition of Pareto Set Approximationp. 236
The Thresholding Approachp. 237
Fairness as Multi-Objective Optimizationp. 241
The Meaning of Fairnessp. 241
Axiomatic Theory of Fairnessp. 242
Application to Two Agent MinSump. 243
Problems with Different Objective Functionsp. 245
Aggregative Fairnessp. 246
Conclusionp. 247
Referencesp. 248
Comparisons of Stochastic Task-Resource Systemsp. 253
Motivationp. 253
Task-Resource Modelsp. 255
Static Systemsp. 255
Dynamic Systemsp. 256
Stochastic Ordersp. 257
Orders for Real Random Variablesp. 258
Orders for Multidimensional Random Variablesp. 263
Associationp. 264
Applications to Static Problemsp. 265
The 1 ¿Ci Problem, Revisitedp. 266
PERT Graphsp. 267
Applications to Dynamic Systemsp. 268
Single Queuesp. 269
Networks of Queuesp. 272
Stochastic Comparisons and Simulation Issuesp. 275
Referencesp. 279
The Influence of Platform Models on Scheduling Techniquesp. 281
Introductionp. 281
Platform Modelingp. 282
Modeling the Topologyp. 282
Modeling Point-to-Point Communication Timep. 284
Heterogeneityp. 288
Modeling Concurrent Communicationsp. 289
Interaction between Communication and Computationp. 291
Scheduling Divisible Loadp. 292
Single Roundp. 293
Multi-Roundp. 296
Iterative Algorithms on a Virtual Ringp. 298
Problem Statementp. 299
Complete Homogeneous Platformp. 299
Complete Heterogeneous Platformp. 300
Arbitrary Heterogeneous Platformp. 301
Data Redistributionp. 302
The Matching Approachp. 304
The Elastic Flows Approachp. 306
Conclusionp. 307
Referencesp. 307
Indexp. 311
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