Edge coloring bipartite multigraphs for dynamically configuring optical switches

Multi-chip graphics processing units (GPUs) interconnected by a photonic network-on-wafer are a promising technology to further increase the performance of GPUs. The network control algorithm managing dynamic bandwidth allocation (DBA) in this network needs to execute very frequently so that resources can be optimally used. This algorithm relies on edge coloring bipartite multigraphs to translate inter-chip bandwidth demands into updated routing tables for the GPU chips and optical switches in the network. In this work, we design fast edge coloring algorithms, both approximate and exact, for bipartite multigraphs. These algorithms are tailored to the high edge multiplicities of the multigraphs in this research. The runtimes are optimized by using efficient data structures and introducing pre- and post-processing. These new algorithms are up to ${20} \times$ faster than the state-of-the-art baseline algorithm. New simulations show that, with such low reconfiguration periods, DBA has the potential to double the performance of a high-traffic GPU workload compared to a static network with the same bandwidth.