  All to all broadcast is a collective communication in a network with the
constraint that every node must send to each other certain piece of its data.
This paper addresses the problem of optimal all port all to all broadcast in
multidimensional tori. The optimality criteria considered are the minimum
exchange steps, no duplicated data in the sense that only new data are conveyed
to receivers and the balance of the communication links load. It is proved that
under these constraints, an optimal broadcast is not feasible in any
multidimensional torus. Then, the tori which are capable of optimal broadcasts
are characterized.
