Efficient bufferless routing on leveled networks

We give near optimal bufferless routing algorithms for leveled networks. N packets with preselected paths are given, and once injected, the packets may not be buffered while in transit to their destination. For the preselected paths, the dilation D is the maximum path length, and the congestion C is the maximum number of times an edge is used. We give two bufferless routing algorithms for leveled networks: (i) a centralized algorithm with routing time O((C + D) log(DN)); (ii) a distributed algorithm with routing time O((C + D) log²(DN)). The distributed algorithm uses a new technique, reverse-simulation, which is used to obtain a distributed emulation of the centralized algorithm. Since a well known lower bound on the routing time is Ω(C + D), our results are at most one or two logarithmic factors from optimal.