Controllers in a software defined network and methods implemented such controllers include forming an auxiliary graph based on a network graph. The network graph includes aggregating and non-aggregating nodes and the auxiliary graph includes a number of non-aggregating nodes based on a number of incoming neighbors to non-aggregating nodes in the network graph. A best path from a source node to a destination node through the auxiliary graph is determined based on output links from non-aggregating nodes are occupied. The best path through the auxiliary graph is translated to a best path from the source node to the destination node through the network graph. Traffic is routed through the software-defined network based on the best path.