Both the Maryland and Syracuse libraries are based on runtime-computed, reusable communication schedules. To a greater or lesser extent the runtime systems sort and coalesce messages to minimize and aggregrate communication on the network. In the compiler domain, Xiaoming Li has proposed a scheme based on shift homomorphism for analysis of HPF forall statements . This scheme classifies the communication needs of these statements. These ideas have been integrated into the Syracuse HPF translation system, as reported in .