For ease of presentation, we describe
the personalized communication algorithm for the case when the input
is initially evenly distributed amongst the processors. The reader is
directed to [4] for the general case. Consider a set of *n*
elements evenly distributed amongst *p* processors in such a manner
that no processor holds more than elements. Each element
consists of a pair , where *dest* is the
location to where the *data* is to be routed. There are no assumptions
made about the pattern of data redistribution, except that no
processor is the destination of more than *h* elements and thus
. We assume for
simplicity (and without loss of generality) that *h* is an integral
multiple of *p*.

helman@umiacs.umd.edu