Distributed and on-line routing on tori

In this paper we study tire problem of assigning paths to packets oil N x N tori in an on-line and distributed fashion. By on-line we mean that the routing decisions must be made without any knowledge of future requests. Being distributed is an equally important feature of our design. for Such algorithms need knot know the global configuration of the network in the process of routing packets. We use the technique of competitive analysis to measure the performance of our design, In addition to showing an Omega(log N) lower bound on the competitive ratio, we present both deterministic and randomized algorithms which are O(log N) competitive with respect to the maximum load (i.e., congestion) on communication links.