On The Optimality Of All To All Broadcast In k ary n dimensional Tori

TL;DR

This paper investigates the limits of all-to-all broadcast efficiency in multidimensional tori networks, proving optimal solutions are impossible under certain constraints and characterizing the tori where optimal broadcasts are feasible.

Contribution

It establishes the impossibility of optimal all-to-all broadcast in multidimensional tori and characterizes the tori that can support such optimal broadcasts.

Findings

Optimal broadcast is not feasible in any multidimensional torus under the given constraints.

Certain tori can support optimal broadcasts, which are characterized in the paper.

The study provides theoretical bounds and conditions for broadcast optimality.

Abstract

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.