Packaging and multiplexing of hierarchical scalable expanders

Abstract

Multistage networks are important in a wide variety of applications. Expander-based networks, such as multibutterflies, are a tremendous improvement over traditional butterflies in both fault and congestion tolerance. However, multibutterflies cost at least twice as much in chips and wiring as butterflies. It is also impossible to build large multi-butterflies due to their wiring complexity. We show that we can build an expander-based network that has comparable cost to a butterfly with the same number of endpoints, yet has substantially better fault and congestion performance. Specifically, we introduce a hierarchical construction that dramatically reduces wiring complexity and makes large expanders buildable. We are able to exploit the hierarchical structure to find large numbers of logical wires to multiplex over a smaller number of physical wires. Since many of the wires in an expander-based network are used to provide alternate paths, not useful bandwidth, substantial multiplexing can be done without significantly degrading performance. We present simulation results to support our conclusions. In comparing a butterfly with the comparable 2-to-1 multiplexed metabutterfly, we found that the metabutterfly performed better by nearly a factor of two on random traffic and greater than a factor of five on worst-case traffic.