Optimal Routing in Binomial Graph Networks

Abstract

A circulant graph with n nodes and jumps j 1 , j 2 , ..., j m is a graph in which each node i, 0 ≤ i ≤ n − 1, is adjacent to all the vertices i ± j k mod n, where 1 ≤ k ≤ m. A binomial graph network (BMG) is a circulant graph where j k is the power of 2 that is less than or equal to n. This paper presents an optimal (shortest path) two-terminal routing algorithm for BMG networks. This algorithm uses only the destination address to determine the next hop in order to stay on the shortest path. Unlike the original algorithms, it does not require extra space for routing tables or additional information in the packet. The experimental results show that the new optimal algorithm is significantly faster than the original optimal algorithm.

Scalable Runtime for MPI: Efficiently Building the Communication Infrastructure

“…We use the underlying launching tree to exchange contact information at the runtime level, and let the runtime system build for itself a communication infrastructure mapping a binomial graph [1] topology. This topology has several interesting properties such as redundant links to support fault tolerance and binomial tree shape connectivity rooted in each peer.…”