Packet Routing in Networks with Long Wires

In this paper, we examine the packet routing problem for networks with wires of di ering length. We consider this problem in a network independent context, in which routing time is expressed in terms of \congestion" and \dilation" measures for a set of packet paths. We give, for any constant > 0, a randomized on-line algorithm for routing any set of N packets in O((C lg (Nd) +D lg(Nd))= lg lg(Nd)) time, where C is the maximum congestion and D is the length of the longest path, both taking wire delays into account, and d is the longest path in terms of number of wires. We also show that for edge-simple paths, there exists a schedule (which could be found o -line) of length O (cd max +D) lg(d max ) lg lg(d max ) , where d max is the maximum wire delay in the network. These results improve upon previous routing results which assume that unit time su ces to traverse a wire of any length. They also yield improved results for job-shop scheduling as long as we incorporate a technical restriction on the job-shop problem.