On The Communication Complexity Of Distributed Name-Independent Routing Schemes

We present a distributed asynchronous algorithm that, for every undirected weighted n-node graph G, constructs name-independent routing tables for G. The size of each table is (O) over tilde(root n), whereas the length of any route is stretched by a factor of at most 7 w.r.t. the shortest path. At any step, the memory space of each node is (O) over tilde(root n). The algorithm terminates in time O(D), where D is the hop-diameter of G. In synchronous scenarios and with uniform weights, it consumes (O) over tilde(root n + n(3/2) min {D, root n}) messages, where m is the number of edges of G.In the realistic case of sparse networks of poly-logarithmic diameter, the communication complexity of our scheme, that is (O) over tilde (n(3/2)), improves by a factor of root n the communication complexity of any shortest-path routing scheme on the same family of networks. This factor is provable thanks to a new lower bound of independent interest.