An apparatus includes a network interface and a processor. The network interface is configured to communicate with a network that includes a plurality of switches interconnected in a Cartesian topology having multiple dimensions. The processor is configured to predefine an order among the dimensions of the Cartesian topology, to search for a preferred route via the network from a source switch to a destination switch, by evaluating candidate routes based at least on respective numbers of switches along the candidate routes for which traversal to a next-hop switch changes from one of the dimensions to another of the dimensions opposite to the predefined order, and to configure one or more of the switches in the network to route packets from the source switch to the destination switch along the preferred route.