An Efficient All-to-all Communication Algorithm for Mesh/Torus Networks

Abstract

An efficient all-to-all communication algorithm for torus and mesh networks, A2AT, was proposed. A2AT schedules message sending sequence so that all links are fully used by exploiting function of concurrent message transfer in the node. By using A2AT, the hop count of messages equals the maximum number of messages sharing a link in their routes for all message transfers. A2AT can therefore maintain synchronization without the need for phasing operation such as an MPI barrier. When the VOQ which is an ideal configuration for A2AT was used, communication times for mesh/torus network obtained by A2AT were roughly 1.20 and 1.09 times higher, on average, than those of the ideal times. When the networks had the minimum number of virtual channels and a small buffer, assuming a practical network, A2AT was able to reduce communication times by 12.5% and 36.0% compared with those of the conventional algorithm. When two controllers are used, A2AT reduced 28.2% and 55.7% communication time with those by A2AND on 15×15×15 (=3,375 nodes) mesh and torus networks respectively (18.6% and 44.8% in average). A2AT also reduced 15.1% and 41.9% of communication time with those by A2AND on the same mesh and torus networks respectively (14.4% and 37.5% in average) when six controllers are used.

Realizing Optimal All-to-All Personalized Communication Using Butterfly-Based Networks

“…In past years, many results have been reported for meshes and tori, that have a simple and regular topology, a bounded node degree and present good scalability, see, e.g., [28], [29], [30], and [31] for meshes and [32], [33], and [34] for tori, and the more recent [35]. In particular, in [28] Scott uses the direct approach, consisting in scheduling direct communication between every pair of processors and shows that, in an a × a mesh, the number of contention-free communication steps must be at least a 3 4 .…”

“…Hence, both direct and indirect approaches reach the lower bound, that for meshes consisting of N processors, is O(N √ N ) time. In [35], an efficient all-toall communication algorithm implemented on a mesh/torus network is presented. The algorithm schedules sending messages in sequence so that all links are fully used and collisions are avoided, thus reducing the communication time with respect to conventional algorithms for all-to-all personalized communication on mesh and torus.…”

Abstract: Visualization Tool for Development of Topology-Aware Network Communication Algorithm

“…Conversely, the links near the destination nodes are drawn in green, which implies higher link utilization and no blocking. Fig.3 shows snapshots of all-to-all communication using a conventional algorithm (upper) and the new algorithm [2] (lower) in a 25 × 25 torus network. We see many blue and green links with the new algorithm, whereas there are some pink links with the conventional algorithm.…”

Dynamic Load Balancing on All-to-All Personalized Communications Using the NNLB Principal

“…Many complicated scientific parallel computing applications exhibit the necessity for all-to-all communication, where every processor has to send a message to all other processors in the network ( [1], [3], [4], [9], [10], [14], [24], [25], [26], [27]). All-to-all communication is divided into two communication patterns: index (or all-to-all personalized communication) and concatenation (or all-to-all broadcast).…”