Mathematical Foundations of Parallel Computing

Front Cover
World Scientific - Computers - 343 pages
Parallel implementation of algorithms involves many difficult problems. In particular among them are round-off analysis, the way to convert sequential programs and algorithms into the parallel mode, the choice of appropriate or optimal computer architect and so on. To solve these problems, it is necessary to know very well the structure of algorithms. This book deal with the mathematical mechanism that permits us to investigate structures of both sequential and parallel algorithms. This mechanism allows us to recognize and explain the relations between different methods of constructing parallel algorithms, the methods of analysing round-off errors, the methods of optimizing memory traffic, the methods of working out the fastest implementation for a given parallel computer and other methods attending the joint investigation of algorithms and computers.
 

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Contents

Chapter
1
Graph of algorithm
16
Chapt
24
Topological sorting
26
Schedules and graph machine
34
Examples
43
32
50
Algorithm Execution Time
55
33
136
Sectioning of memory
143
Matrix Investigation of Algorithm Structure
155
Recovering the linear functional
164
Roundoff error analysis
174
Examples
186
Functional Investigation of Algorithm Structure
193
Regular graphs
203

Number semirings and other sets
67
Minimax properties of schedules
80
Optimal and highspeed schedules
89
Examples
100
Algorithms and Computer Memory
107
Total required memory size
120
Hierarchical memory
135
35
208
Afterword
215
References
333
80
339
Index
341
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