A computer system includes compute nodes coupled through a switch to shared or non-shared I/O devices. The switch includes a pool of bridge headers and virtual bridges coupling a root port of a compute node to each of one or more shared or non-shared I/O devices. The switch is configured to associate each of the virtual bridges with a respective one of the fixed pool of bridge headers, receive a packet including data identifying the root port and a shared or non-shared I/O device, and route the packet in response to comparing data in the packet to data in the bridge headers associated with the virtual bridges. The virtual bridges comprise a hierarchy of virtual bridges in which one virtual bridge connects the root port to the remaining virtual bridges of the hierarchy. The switch may change the associations between virtual bridges and bridge headers.