Space-Efficient Message Routing in c-Decomposable Networks

Message routing strategies are given for any network that can be decomposed by a separator of size at most a small constant c into two networks with the same property. These strategies use a total of O(cnlogn) items of routing information, keep node names to O(log n) bits, and still route along near-shortest paths. If the names generated from a separator-based hierarchical decomposition of the network alone are used, then the routing between any pair of nodes is along a path that is at most 3 times longer than an optimal path. By augmenting the node names with O(clogclogn) additional bits, the length of any message path is improved to (2/ex) + 1 times the length of an optimal path, where a > 1 is the positive root of the equation a r{c+l)/21 ex 2 = o.