In this article, we address the problem of finding an optimal schedule for all-to-all personalized message communication among the processors in a multiprocessor system where every processor has a unique message for every other processor. When there are
n
processors and ⌊
n
/2⌋ parallel databus or channels for message communications, there exist algorithms that require
O
(
n
2
) time for assigning the databus/channels to the processor-pairs to obtain a schedule with minimum number of time slots. However, in recent massively parallel processing systems with a huge number of processors, the number
k
of available databus/channels is usually much smaller than ⌊
n
/2⌋. Thus, in each round of communication, only
k
processor-pairs (
k
< ⌊
n
/2⌋) can exchange their messages in parallel. We address this general case of all-to-all personalized communication and present a new technique for scheduling the channels among processor-pairs where only
k
< ⌊
n
/2⌋ databus/channels are available. We show that the proposed technique is optimal for all values of
n
other than 2
k
<
n
< 3
k
. For 2
k
<
n
< 3
k
, we show that the required number of rounds may be more than the lower bound of ⌈
n
/(
n
−1)2
k
⌉ by at most 11%, and proving the optimality of our technique remains as an open problem in this case.