17 research outputs found
A note on vertex-transitive non-Cayley graphs from Cayley graphs generated by involutions
AbstractWe show that the result of Watkins (1990) [19] on constructing vertex-transitive non-Cayley graphs from line graphs yields a simple method that produces infinite families of vertex-transitive non-Cayley graphs from Cayley graphs generated by involutions. We also prove that the graphs arising this way are hamiltonian provided that their valency is at least six
FatPaths: Routing in Supercomputers and Data Centers when Shortest Paths Fall Short
We introduce FatPaths: a simple, generic, and robust routing architecture
that enables state-of-the-art low-diameter topologies such as Slim Fly to
achieve unprecedented performance. FatPaths targets Ethernet stacks in both HPC
supercomputers as well as cloud data centers and clusters. FatPaths exposes and
exploits the rich ("fat") diversity of both minimal and non-minimal paths for
high-performance multi-pathing. Moreover, FatPaths uses a redesigned "purified"
transport layer that removes virtually all TCP performance issues (e.g., the
slow start), and incorporates flowlet switching, a technique used to prevent
packet reordering in TCP networks, to enable very simple and effective load
balancing. Our design enables recent low-diameter topologies to outperform
powerful Clos designs, achieving 15% higher net throughput at 2x lower latency
for comparable cost. FatPaths will significantly accelerate Ethernet clusters
that form more than 50% of the Top500 list and it may become a standard routing
scheme for modern topologies
Slim Fly: A Cost Effective Low-Diameter Network Topology
Abstract—We introduce a high-performance cost-effective net-work topology called Slim Fly that approaches the theoretically optimal network diameter. Slim Fly is based on graphs that approximate the solution to the degree-diameter problem. We analyze Slim Fly and compare it to both traditional and state-of-the-art networks. Our analysis shows that Slim Fly has significant advantages over other topologies in latency, bandwidth, resiliency, cost, and power consumption. Finally, we propose deadlock-free routing schemes and physical layouts for large computing centers as well as a detailed cost and power model. Slim Fly enables constructing cost effective and highly resilient datacenter and HPC networks that offer low latency and high bandwidth under different HPC workloads such as stencil or graph computations. I