Optimal Routing in Toroidal Networks

In this paper we study routing algorithms for one-to-one communication in multiprocessors, 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 Keywords: optimal routing, multiprocessors, toroidal networks 1 Introduction Toroidal interconnection networks are becoming the standard interconnection networks for multiprocessors [6, 5, 7]. Figure 1 shows a two-dimensional toroidal network. An extensive comparative analysis of the latency in such networks was done by Dally in [7]. An optimal dynamic routing policy was presente..