On bit-serial packet routing for the mesh and the torus

Abstract

The bit-serial routing problem wherein each packet consists of a sequence of k flits and is thus called a snake, is considered. On the basis of the properties of the snake during the routing, a formal definition is given for three different packet routing models, namely, the store-and-forward model, the cut-through model, and the wormhole model. The wormhole model, which is most commonly used in practice, is studied. The first algorithms (deterministic and probabilistic) based on the wormhole model for the permutation routing problem on a chain, on a square mesh, and on a square torus are given. A new lower bound is derived for distance-limited permutation routing on a ring of processors, and an algorithm that matches this lower bound if the packets are routed independently is given.<>