Process mapping asks to assign vertices of a task graph to processing elements of a supercomputer such that the computational workload is balanced while the communication cost is minimized. Motivated by the recent success of GPU-based graph partitioners, we propose two GPU-accelerated algorithms for this optimization problem. The first algorithm employs hierarchical multisection, which partitions the task graph alongside the hierarchy of the supercomputer. The method utilizes GPU-based graph partitioners to accelerate the mapping process. The second algorithm integrates process mapping directly into the modern multilevel graph partitioning pipeline. Vital phases like coarsening and refinement are accelerated by exploiting the parallelism of GPUs. In our experiments, both methods achieve speedups exceeding 300 when compared to state-of-the-art CPU-based algorithms. The first algorithm has, on average, about 10 percent greater communication costs and thus remains competitive to CPU algorithms. The second approach is much faster, with a geometric mean speedup of 77.6 and peak speedup of 598 at the cost of lower solution quality. To our knowledge, these are the first GPU-based algorithms for process mapping.

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