1. A parallel computer comprising a plurality of processing nodes interconnected by a control network and a data router, wherein: (a) each processing node comprises a data router interface, a control network interface, and a processor, each processor being either a scalar processor or a processing element; (b) the control network comprises a plurality of network nodes arranged in a fat-tree structure for transferring program commands and status information between the processing nodes, whereby each processing node can transfer program commands and status information to every other processing node through the control network; (c) the data router comprises a plurality of router nodes arranged in a fat-tree structure for transferring data packets between the processing nodes, whereby each processing node can transfer data packets to every other processing node through the data router; (d) one of the scalar processors comprises means for periodically issuing a context switch command to initiate a context switch causing the parallel computer to switch from a first user program in a first context to a second user program in a second context; (e) the data router comprises means for replacing data packets relating to the first context with data packets relating to the second context in each router node in response to the context switch command; (f) the control network comprises means for replacing program commands and status information relating to the first context with program commands and status information relating to the second context in each network node in response to the context switch command; and (g) each processing node comprises means for replacing internal data relating to the first context with internal data relating to the second context in response to the context switch command.