Fault tolerant and load balanced routing

Techniques are described for balancing traffic load for networks configured in multi-rooted tree topologies, in the presence of link failures. Maximum flows (through minimum cuts) are calculated for subgraphs that incorporate effective link capacities on links between source and destination nodes. Effective link capacities may be determined that take into account link failures, as well as sharing of current available link capacities by multiple nodes. Traffic is balanced while simultaneously fully utilizing available link capacities, even available link capacities on partially failed links (e.g., partially failed Link Aggregation Groups (LAGs)).