Mathematical Foundations of Parallel Computing

Mathematical Foundations of Parallel Computing

Valentin V. Voevodin

Language: English

Pages: 362

ISBN: 2:00362151

Format: PDF / Kindle (mobi) / ePub


Parallel implementation of algorithms involves many difficult problems. In particular among them are round-off analysis, the way to convert sequential programmes and algorithms into parallel mode, the choice of appropriate or optimal computer architect and so on. To solve the stumbling blocks of these problems it is necessary to know the structure of algorithms very well. The book treats 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, methods to analyze round-off errors, methods to optimize memory traffic, methods to work out the fastest implementation for a given parallel computer and other methods attending the joint investigation of algorithms and computers.

 

 

 

 

 

 

 

 

 

 

 

layers and t h e of the parallel to parallelism i n the equi- i n the particular research field. The number number o f l a y e r s o f nodes layer width allel form height. maximum length width "maximum" parallel form i s the layer's We w i l l i s called t o t h e same parallei i f at algorithm from computation. the width of the i t h that par- of algorithm. some The A least one path layer, and a l l of input layer. make u s e o f b o t h r e s e a r c h i

each macrograph would parallel nodes. They to the coordinate partition not subgraph n o t be a c y c l i c a l g o r i t h m (12.3) memory belonged time exchanges crease o f t h e o v e r a l l entirely other entirely levels. are to a I n other these data t o be e x e c u t e d several consecutive level. t o some without level t o schedule macronodes. partitionings do considerable i n - l e t some s u b g r a p h b e - o f data i t exchanges with t o t h e

necessarily require that T h i s memory must c o n t a i n a l l i n - i n c l u d e e . g . many used to solve the methods small some execu- time required to exist amount implicit the computational of that RAM ones (like physics prob- lems. N o t e t h a t d i f f e r e n t demands a s t o t h e s t r u c t u r e are not d i r e c t l y of computations ference connected w i t h the (im)possibility at the individual arithmetic Thus size operations level. i n t h e

i s t i c basing because t o comprehend a l l shall determine of after first. architecture h e l p one the f o r i t points studying the set of number o f f u n c t i o n a l as e t c . T h e n we computer models, im- time, will while characteristics. the plan carrying i s t o be ever By only investigation the c h a r a c t e r i s t i c s machine the achieved r i t h m s . Now problem, of algorithms. computer, p r i m a r i l y t h e g r a p h m a c h i n e we

12.1 e v e r y described vide and partitioning corresponds of the algorithm to a partial b y ( 1 6 . 1 ) . t h e v a l u e s H. H. L now b e i n g graph. Besides, sults subgraph the arrays also belonging explicit A , B, a n d C now s t o r e graph I n algorithm also t h e s i z e s o f t h e subt h e i n p u t d a t a and r e - t o t h e s u b g r a p h . These i n p u t d a t a and r e s u l t s i n f o r m a t i o n o n w h a t d a t a may be s t o r e d w h a t c a n be g a

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