Upper and lower bounds for routing schemes in dynamic networks

An algorithm and two lower bounds are presented for the problem of constructing and maintaining routing schemes in dynamic networks. The algorithm distributively assigns addresses to nodes and constructs routing tables in a dynamically growing tree. The resulting scheme routes data messages over the shortest path between any source and destination, assigns addresses of O(log²n) bits to each node, and uses in its routing table O(log³n) bits of memory per incident link, where n is the final number of nodes in the tree. The amortized communication cost of the algorithm is O(log n) messages per node. Also given are two lower bounds on the tradeoff between the quality of routing schemes (i.e., their stretch factor) and their amortized communication cost in general dynamic networks.