Section: New Results

Multi-criteria graph partitioning for multi-physics simulations load balancing

A new set of algorithms has been designed to compute multi-criteria static mappings for the load balancing of multi-phisics simulations. The multi-criteria graph partitioning is known to be NP-hard, and there exist very few multi-criteria graph partitioners. Moreover, they focus on the edge-cut minimization instead of enforcing load balance. In practice, this strategy often leads to very unbalanced partitions, which are not useful for multi-physics simulations.

We have designed algorithms that focus on balancing several criteria at the same time to ensure that our results always match all balance criteria. We have implemented a prototype in Python to test these different heuristics. One of them, called PIERE, obtained good results [15], in term of balance as well as communication costs. PIERE uses the classic multilevel framework, but implements a new initial partitioning algorithm, which allows to find a balanced partition of the graph. The partition is then refined by local optimization heuristics that ensure the balance is kept for all criteria. This allow us to return a partition respecting the balance constraints. In [15], we compare against well-known partitioners that are Scotch and METIS , and highlight that, for a small mesh, the results exhibit a high discrepancy: each tool lacks of robustness.

PIERE outperformed the existing software METIS in our test cases, but there is room for improvement. We also verified the superiority of the hypergraph model over the graph model used by most partitioners. Meanwhile, we studied the source code of well known partitioners, namely METIS and Scotch , and we have identified a lot of algorithmic choices and internal parameters that are not described in their documentations. Carefully analyzing them helps us to clearly understand the differences of the different algorithms.