Solutions to Parallel and Distributed Computing Problems: Lessons from Biological Sciences
by Albert Y. Zomaya, Fikret Ercal, Stephan Olariu
7.2. MULTIPROCESSOR SCHEDULING
A multiprocessor system is represented by an undirected, unweighted graph, Gs = (Vs, Es) called a system graph. The set of Ns nodes, Vs of the system graph represents processors with their local memories of a parallel computer of multiple-instruction, multiple-data (MIMD) architecture. The set of edges, Es represents bidirectional channels between processors and defines a topology of the multiprocessor system. Figure 7.1a shows an example of a system graph representing a multiprocessor system consisting of two processors P0 and P1. This topology will be used in all experiments presented in this work. It is assumed that all processors have the same computational power, and that communication via links does not consume any processor time.
A parallel program is represented by a weighted directed acyclic graph Gp = (Vp, Ep), called a precedence task graph or a program graph. The set of Np nodes, Vp of the graph represents elementary tasks, which are indivisible computational units. There exists a precedence constraint relation between tasks k and l in the precedence task graph if the output produced by task k has to be communicated to task l.
A program graph has two attributes: weights bk and akl. Weights bk of the nodes describe the processing time (computational cost) needed to execute a given task on any processor of a given multiprocessor system. The set of edges, Ep of the precedence task graph describes the communication pattern between the tasks. ...
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