Rapid Calculation of Max-Min Fair Rates for Multi-Commodity Flows in Fat-Tree Networks

Max-min fairness is often used in the performance modeling of interconnection networks. Existing methods to compute max-min fair rates for multi-commodity flows have high complexity and are computationally infeasible for large networks. In this work, we show that by considering topological features, this problem can be solved efficiently for the fat-tree topology that is widely used in data centers and high performance compute clusters. Several efficient new algorithms are developed for this problem, including a parallel algorithm that can take advantage of multi-core and shared-memory architectures. Using these algorithms, we demonstrate that it is possible to find the max-min fair rate allocation for multi-commodity flows in fat-tree networks that support tens of thousands of nodes. We evaluate the run-time performance of the proposed algorithms and show improvement in orders of magnitude over the previously best known method. We further demonstrate a new application of max-min fair rate allocation that is only computationally feasible using our new algorithms.