Improved algorithms for partitioning tree and linear task graphs on shared memory architecture

In parallel and distributed computing, the overall system performance is significantly influenced by how a task graph representing an application is mapped onto a specific multiprocessor topology. In this paper, algorithms with improved performance are proposed to map tree and linear task graphs onto shared memory multiprocessing architectures. Specifically, the task graphs are partitioned with our algorithms so that the load is balanced, processor utilisation is maximized, and the communication demand on the interconnection network is minimized in a shared memory multiprocessor. All the proposed algorithms are polynomial in time complexity. Bottleneck and processor minimization algorithms of this type are proposed. The bandwidth minimization algorithm has a complexity of O(n + p log q) (q⩽p⩽n), in contrast with the complexity of O(n log n) for the best known algorithm in the literature. Furthermore, we have identified cases where our algorithm will run in linear time on the average