All-To-All Personalized Communication in Wormhole-Routed 2D/3D Meshes and Multidimensional Interconnection Networks

All-to-all personalized communication,or complete exchange,is at the heart of numerous applications in paral-lel computing.It is one of the most dense communication patterns.In this paper,we consider this problem in a2D/3D mesh and a multidimensional interconnection network with the wormhole-routing capability.We propose complete ex-change algorithms for them respectively.We propose O(mn 2 )phase algorithm for2D mesh P m ×P n and O(mn 2 l 2 )phase algo-rithm for3D mesh P m ×P n ×P l ,where m,n,l are any positive integers.Also O(ph(G 1 )n 2 )phase algorithm is proposed for a multidimensional interconnection network G 1 ×G 2 ,where ph(G 1 )stands for complete exchange phases of G 1 and|G 2 |=n.