Algorithms for all-to-all personalized exchange in 2D and 3D tori

The inter-processor all-to-all communication patterns can be found in many important parallel algorithms. This paper presents new algorithms for all-to-all personalized exchange for circuit switched or wormhole routed 2D and 3D torus connected multiprocessors. The algorithms use message combining to minimize message startups at the expense of larger message sizes. The unique feature of these algorithms is that they are the first algorithms that we know of that operate in a bottom-up fashion rather than a recursive top-down manner.