Exploiting the Block Structure of the Web for Computing
The web link graph has a nested block structure: the vast majority of hyperlinks link pages on a host to other pages on the same host, and many of those that do not link pages within the same domain. We show how to exploit this structure to speed up the computation of PageRank by a 3-stage algorithm whereby (1)~the local PageRanks of pages for each host are computed independently using the link structure of that host, (2)~these local PageRanks are then weighted by the ``importance'' of the corresponding host, and (3)~the standard PageRank algorithm is then run using as its starting vector the weighted aggregate of the local PageRanks. Empirically, this algorithm speeds up the computation of PageRank by a factor of 2 in realistic scenarios. Further, we develop a variant of this algorithm that efficiently computes many different ``personalized'' PageRanks, and a variant that efficiently recomputes PageRank after node updates.