1. A logical network comprising: a plurality of host machines implementing a logical routing element (LRE), each host machine operating a set of virtual machines (VMs) and a managed physical routing element (MPRE) for routing data packets from the VMs operating on the host machine to network nodes in the logical network in order to implement the LRE; and a plurality of physical machines that are external to the host machines, the plurality of physical machines not implementing the LRE, wherein multiple MPREs in a subset of the plurality of host machines are selected for (i) responding to address resolution protocol (ARP) messages sent by the physical machines and (ii) performing L3 routing on data packets from the plurality of physical machines to the VMs operating on the host machines.