PageRank: Three Distributed Algorithms

This paper shows for the first time that there are multiple PageRank definitions, and that more is required to justify PageRank than is offered in the literature ([1], [2] and [5]). Adopting a formal approach, this paper provides a justification of PageRank. It also shows that the irreducibility restriction on the PageRank transition matrix [5] is unnecessary. This is important because it gives the personalisation vector more intuitive force. Noting the difficulties in calculating PageRank centrally, the paper then shows, via the ChazanMiranker theorem [10], that distributed calculation algorithms are possible; and, it presents three such novel algorithms. The first of these takes documents / pages as being of principal interest; the second and third, in an attempt to reduce communication overheads, focus attention on nodes/ webservers. Empirical test results are shown. These confirm reduced message numbers for algorithms 2 and 3. They also show that more investigation is required into suitable -thresholds within asynchronous environs.