Four Algorithms on the Swapped Dragonfly

TL;DR

This paper explores four algorithms on the Swapped Dragonfly network, demonstrating their efficiency and conflict-free operation, and compares them with algorithms on hypercubes and fully populated Dragonflies.

Contribution

It introduces four algorithms tailored for the Swapped Dragonfly network, analyzing their performance and applicability, and establishing their advantages over existing network algorithms.

Findings

Matrix multiplication in sqrt(n) rounds for perfect square K

All-to-all exchange in n/s rounds when K and M share a factor s

Broadcast in 3x/M rounds with synchronized headers

Abstract

The Swapped Dragonfly with M routers per group and K global ports per router is denoted D3(K;M) [1]. It has n=KMM routers and is a partially populated Dragonfly. A Swapped Dragonfly with K and M restricted is studied in this paper. There are four cases. matrix product: If K is a perfect square, a matrix product of size n can be performed in squareroot n rounds. all-to-all exchange: If K and M have a common factor s, an all-to-all exchange can be performed in n/s rounds. broadcast: If D3(K,M) is equipped with a synchronized source-vector header it can perform x broadcast in 3x/M rounds. ascend-descend: If K and M are powers of 2 an ascend-descend algorithm can be performed at twice the cost of the algorithm on a Boolean hypercube of size n. In each case the algorithm on the Swapped Dragonfly is free of link conflicts and is compared with algorithms on a hypercube as well as on the fully populated Dragonfly. The results on the Swapped Dragonfly are more applicable than the special cases because D3(K,M) contains emulations of every Swapped Dragonfly with J less than equal to K and/or L less than or equal to M. Keywords: Swapped Interconnection Network, Matrix Product, All-to-all, Universal Exchange, Boolean Hypercube, Ascend-descend algorithm, Broad- cast, Edge-disjoint spanning tree. References [1] R. Draper. The Swapped Dragonfly , ArXiv for Computer Science:2202.01843. 1