Distributed Recommender Systems and the Network Topologies that Love Them

One approach to distributed recommender systems is to have users sample products at random and randomly query one another for the best item they have found. We have been considering refinements to this approach that take advantage of a communication network; users may share information only with their immediate neighbors, who either by design or by nature may have common interests. In the “mailing list model,” users with common interests form cliques, while in the “word-of-mouth model” the users are distributed randomly in a scale-free network (SFN). In both models, users tell their neighbors about satisfactory products as they are found. We have found that our distributed recommender systems benefit from the communication network in terms of the number of sampled items, the number of messages sent, and the amount of “spam” sent. In the course of developing these results, we have revisited the question of subgraph structure in SFNs and now have a more precise understanding of the character and parameters of random SFN subgraphs than has previously been published. This new result in power-law graphs gives a clearer picture of the resilience of SFNs to random node failures; in fact, their resilience appears to have been overstated in the literature. In the case of the widely-cited “Internet resilience” result, high failure rates actually lead to the orphaning of half or more of the surviving nodes and the complete disintegration of the giant component after 90% of the network has failed independently of the size of the network.