Exploiting symmetry for partitioning models in parallel discrete event simulation

Abstract

We investigated the benefit of exploiting the symmetries of graphs for partitioning. We represent the model to be simulated by a weighted graph. Graph symmetries are studied in the theory of permutation groups and can be calculated in polynomial time with the nauty algorithm by B. McKay (1981). We designed an algorithm to extract useful symmetries from the automorphism group, which can be used to create partitions derived from the graph's structure. Our approach is focused on composite graphs, for which identical subgraphs reoccur in the graph. If these identical subgraphs can be mapped onto each other by symmetries, the subgraphs are replaced by equivalent multivertices, resulting in a 'natural' aggregation of vertices. This approach is applied to parallel simulation of a detailed IP-switch with a conservative synchronous algorithm. The experimental results show that even for good partitions, global and temporal load imbalances are inevitable.