How much can hardware help routing?

We study the extent to which complex hardware can speed up routing. Specifically, we consider the following questions. How much does adaptive routing improve over oblivious routing? How much does randomness help? How does it help if each node can have a large number of neighbors? What benefit is available if a node can send packets to several neighbors within a single time step? Some of these features require complex networking hardware, and it is thus important to investigate whether the performance justifies the investment. By varying these hardware parameters, we obtain a hierarchy of time bounds for worst-case permutation routing. General Terms: Algorithms, Theory Additional Key Words and Phrases: Multi-port, packet routing, permutation routing, randomized routing algorithms, single-port.