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.