Edge-Disjoint Spanning Trees on Star-Product Networks

TL;DR

This paper investigates the construction of edge-disjoint spanning trees in star-product network topologies, which are crucial for improving fault tolerance, communication efficiency, and network resilience in scalable graph structures.

Contribution

It introduces novel methods for constructing maximum or near-maximum edge-disjoint spanning trees in star-product topologies, analyzing their depth properties and practical benefits.

Findings

Constructed EDSTs with maximum or near-maximum cardinality.

Analyzed depth properties of the EDSTs.

Demonstrated benefits for fault tolerance and communication.

Abstract

A star-product operation may be used to create large graphs from smaller factor graphs. Network topologies based on star-products demonstrate several advantages including low-diameter, high scalability, modularity and others. Many state-of-the-art diameter-2 and -3 topologies~(Slim Fly, Bundlefly, PolarStar etc.) can be represented as star products. In this paper, we explore constructions of edge-disjoint spanning trees~(EDSTs) in star-product topologies. EDSTs expose multiple parallel disjoint pathways in the network and can be leveraged to accelerate collective communication, enhance fault tolerance and network recovery, and manage congestion. Our EDSTs have provably maximum or near-maximum cardinality which amplifies their benefits. We further analyze their depths and show that for one of our constructions, all trees have order of the depth of the EDSTs of the factor graphs, and for all other constructions, a large subset of the trees have that depth.