  There are several ideas being used today for Web information retrieval, and
specifically in Web search engines. The PageRank algorithm is one of those that
introduce a content-neutral ranking function over Web pages. This ranking is
applied to the set of pages returned by the Google search engine in response to
posting a search query. PageRank is based in part on two simple common sense
concepts: (i)A page is important if many important pages include links to it.
(ii)A page containing many links has reduced impact on the importance of the
pages it links to. In this paper we focus on asynchronous iterative schemes to
compute PageRank over large sets of Web pages. The elimination of the
synchronizing phases is expected to be advantageous on heterogeneous platforms.
The motivation for a possible move to such large scale distributed platforms
lies in the size of matrices representing Web structure. In orders of
magnitude: $10^{10}$ pages with $10^{11}$ nonzero elements and $10^{12}$ bytes
just to store a small percentage of the Web (the already crawled); distributed
memory machines are necessary for such computations. The present research is
part of our general objective, to explore the potential of asynchronous
computational models as an underlying framework for very large scale
computations over the Grid. The area of ``internet algorithmics'' appears to
offer many occasions for computations of unprecedent dimensionality that would
be good candidates for this framework.
