Optimal Routing in Toroidal Networks

In this paper we study routing algorithms for one-to-one communication in multi-processors, whose interconnection networks have toroidal structure. A toroidal network is an n-dimensional rectangular mesh with additional edge-to-edge connections. Mathematically speaking, these networks are undirected graphs obtained by cartesian product of cycles. We show, that a broad class of routing algorithms, called homogeneous, is optimal for certain class of such networks. Besides, we propose a transformation, which transforms non-optimal homogeneous routing algorithms into optimal semi-homogeneous routing algorithms. 1