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Basic Communication Algorithms and Gaussian Elimination on a Clustered Torus

During the execution of many algorithms on parallel computers certain basic communication patterns are to be followed in order to exchange data between different processors. For example one processor has to send a single message to all the other processors or all processors have to send a message to every other processor. It is obvious that the execution speed of a certain algorithm highly depends on the inter processors communication speed and therefore on the processor interconnection network. Recently, a new network topology has been presented, the clustered torus. The clustered torus is a network topology which has the same advantages as the mesh and the torus, such as their regular structure, allowing for simple routing of messages and their easy scalability. However, with a small number of extra links, a much smaller diameter and average distance are achieved. In this report we investigate the time complexities of some of the most important basic communication algorithms when executed on torus and clustered torus interconnection networks. In particular we show that, if the communication traffic does not become too massive, the clustered torus has a better performance than the torus interconnection network for all the basic communication algorithms we considered. We also evaluate the performance of an implementation of the Gaussian elimination algorithm on a parallel computer built on the clustered torus interconnection network.