By Shahid H. Bokhari
This ebook has been written for practitioners, researchers and stu dents within the fields of parallel and allotted computing. Its goal is to supply distinct assurance of the functions of graph theoretic tech niques to the issues of matching assets and necessities in multi ple desktops. there was massive study during this region over the past decade and excessive paintings maintains while this can be being written. For the practitioner, this publication serves as a wealthy resource of answer strategies for difficulties which are repeatedly encountered within the genuine global. Algorithms are awarded in adequate aspect to allow effortless implementa tion; heritage fabric and primary suggestions are coated in complete. The researcher will discover a transparent exposition of graph theoretic tech niques utilized to parallel and disbursed computing. examine effects are lined and plenty of hitherto unpublished spanning the decade effects by means of the writer are integrated. there are lots of unsolved difficulties during this field-it is was hoping that this publication will stimulate extra research.
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Additional resources for Assignment Problems in Parallel and Distributed Computing
We call these external edges; the original edges of the program graph are called internal edges. 1. These represent the communication costs. The execution costs are placed on the external edges as follows. The edge connecting node i to node P I is labeled with the cost of executing module i on processor P 2 and vice-versa. 2, the edge joining node A and PI is labeled with the cost of executing module A on processor 2. This reversal of labeling is intentional-its importance will become evident in the following discussion.
9. 9 An alternative dynamic assignment graph. previous section this graph is such that every module may execute during some time or the other during a phase. Similarly every pair of modules may communicate during a phase. 9 is in fact a sequence of static graphs connected by relocation cost edges. A mincut in this graph will correspond to the optimal dynamic assignment and can be found using the same network flow algorithms as before. 4. Resource Partitioning with Replication We now turn to a partitioning problem that involves not only programs or program modules, but also physical resources such as line printers, plotters etc.
The best known algorithms are those by Edmonds & Karp (72), Dinic (70) and Karzanov (74) which respectively have O(ne2 ), O(n 2e) and O(n3) complexity, for a graph with n nodes and e edges. Many other algorithms have been developed, as discussed by Even (73,79), Hu (82), Yao (82) and Tarjan (83): these are useful only for very large, sparse graphs*. 5. Trees A special subclass of graphs called Trees will be used in some of the following chapters and needs to be discussed briefly. A tree may be directed or undirected.
Assignment Problems in Parallel and Distributed Computing by Shahid H. Bokhari