made with a small probability. This probability was proportional to the value of making the switches. Another possible metaheuristic optimization method is a tabu search, which adds a memory to the swap decision. In its most simplistic form, a limited history of past swaps is remembered so that they will be excluded from the list of possible swapping nodes. This method for constructing a reference base can also be adapted to distributed settings, where decisions can only be made at the level of individual nodes who have no knowledge of the overall network. It turns out that the only modification necessary is in the method for selecting pairs of random nodes. In a distributed setting, this is done by having each node periodically send out a random walker terminating at a node to be considered for swapping. The Kleinberg model The Kleinberg model of a network is effective at demonstrating the effectiveness of greedy small world routing. The model uses an n x n grid of nodes to represent a network, where each node is connected with an undirected edge to its neighbors. To give it the "small world" effect, a number of long range edges are added to the network that tend to favor nodes closer in distance rather than farther. When adding edges, the probability of connecting some random vertex to another random vertex w is proportional to , where is the clustering exponent. Greedy routing in the Kleinberg model It is easy to see that a greedy algorithm, without using the long range edges, can navigate from random vertices on the grid in time. By following the guaranteed connections to our neighbors, we can move one unit at a time in the direction of our destination. This is also the case when the clustering component is large and the "long range" edges end up staying very close; we simply do not take advantage of the weaker ties in this model. When , the long range edges are uniformly connected at random which means the long range edges are "too random" to be used efficiently for decentralized search. Kleinberg has shown that the optimal clustering coefficient for this model is , or an inverse square distribution. To reason why this is the case, if a circle of radius r is drawn around the initial node it will have nodal density where n is the number of nodes in