The Good , the Bad , the Ugly , and the Beautiful ( P 2 P Authority Computation with Malicious Peers , its Problems , and a Solution )

Computing authority, trust, and reputation scores in web graphs and social networks, by means of eigenvector analysis,is computationally expensive and potentially critical regarding autonomy and privacy of data owners. Embedding the computation in a peer-to-peer network addresses these issues, using distributed algorithms. However, the necessary data exchanges between peers give rise to the problem that malicious peers may cheat in order to manipulate the outcome of the global computation. We present a robust, distributed algorithm for computing authority scores by power-iteration for principal eigenvectors, with resilience to such misbehavior, based on general principles of replication and randomization. Our solution is very general; we merely assume that the fraction of dishonest peers is bounded and there is an unforgeable mechanism for checking peer identities using standard techniques from cryptography. We prove that, with high probability, our algorithm converges to the correct result that the honest peers alone would compute. We also prove a lower bound on the communication complexity showing that the total amount of data that needs to be exchanged is at least linear in the total number of entities of which we wish to compute the authority scores. This holds even in the case when peers are concerned with retrieving the entity whose score is at least a constant fraction of the top-entity score. Experimental studies, with an excerpt of the Librarything social-tagging forum, demonstrate the practical viability and good performance of our algorithm.