Random Regular Graph and Generalized De Bruijn Graph with k-Shortest Path Routing

Abstract

Random regular graph (RRG) has recently beenproposed as an interconnect topology for future large scaledata centers and HPC clusters. While various studies havebeen performed, this topology is still not well understood. RRGis a special case of directed regular graph (DRG) where eachlink is unidirectional and all nodes have the same number ofincoming and outgoing links. In this work, we establish boundsfor DRG on diameter, average k-shortest path length, and aload balancing property with k-shortest path routing, and usethese bounds to evaluate RRG. The results indicate that RRGwith k-shortest path routing is not ideal in terms of diameterand load balancing. We further consider the Generalized DeBruijn Graph (GDBG), a deterministic DRG, and prove thatfor most network configurations, GDBG is near optimal interms of diameter, average k-shortest path length, and loadbalancing with a k-shortest path routing scheme. Finally, weexplore the strengths and weaknesses of RRG for differenttraffic conditions by comparing RRG with GDBG.