1. A switching device comprising: a first memory element associated with a first plurality of output ports, wherein the first memory element includes shared storage configured to store packets received by ones of a first plurality of input ports that are destined to any of the first plurality of output ports; a second memory element associated with a second plurality of output ports, wherein the second memory element includes shared storage configured to store packets received by ones of the first plurality of input ports that are destined to any of the second plurality of output ports; and a first router configured to route first and second packets respectively received by first and second given ones of the first plurality of input ports to the first memory element in response to determinations that the received first and second packets specify destinations corresponding to a same one of the first plurality of output ports; and wherein the first router is configured to route third and fourth packets respectively received by the first and second given ones of the first plurality of input ports to the second memory element in response to determinations that the received third and fourth packets specify destinations corresponding to a same one of the second plurality of output ports.