Global communication algorithms for Cayley graphs

TL;DR

This paper explores efficient communication algorithms for symmetric network topologies modeled by Cayley graphs, focusing on minimizing time for key collective operations like broadcast, accumulation, exchange, and summation.

Contribution

It introduces new algorithms and bounds for communication tasks on Cayley graph-based networks, enhancing understanding of their efficiency and limitations.

Findings

Optimal algorithms for broadcast and summation on Cayley graphs

Reduced communication times compared to previous methods

Theoretical bounds established for various network sizes

Abstract

We discuss several combinatorial problems that arise when one looks at computational algorithms for highly symmetric networks of processors. More specifically, we are interested in minimal times associated with four communication tasks (defined more precisely below): universal broadcast, every processor has a vector that it wishes to broadcast to all the others; universal accumulation, every processor wishes to receive the sum of all the vectors being sent to it by all the other processors; universal exchange, every processor wishes to exchange a vector with each other processor; and global summation, every processor wants the sum of the vectors in all the processors