1. In a message passing multiprocessor network configured as an initial hierarchical tree of processing nodes, a method of overlaying onto the initial tree one or more other hierarchically structured virtual trees of processing nodes for concurrently performing parallel processing operations on one or more data processing problems, said method comprising the steps of transmitting via the initial tree tree connect messages from leaf nodes of the initial tree that are to become members of a second tree to a root node of the initial tree via intermediate parent nodes of the initial tree, said tree connect messages identifying the second tree, and updating status information at each node transmitting and receiving a connect message to reflect the transmittal or receipt of the message and the identity of the second tree, transmitting acknowledge messages from the root node of the initial tree to the leaf nodes of the second tree in response to receipt at the root node of the connect messages from the leaf nodes, and updating status information at each node transmitting and receiving an acknowledge message to reflect the transmittal or receipt of the message and the identity of the second tree, whereby said second tree is established when all of its leaf nodes have received an acknowledge message and whereby individual nodes of the second tree may be addressed by messages containing the identity of the second tree.