d Abstract) Paolo Boldi† Massimo Santini‡ Sebastiano Vigna∗ Deciding which kind of visit accumulates high-quality pages more quickly is one of the most often debated issue in the design of web crawlers. It is known that breadth-first visits work well, as they tend to discover pages with high PageRank early on in the crawl. Indeed, this visit order is much better than depth first, which is in turn even worse than a random visit; nevertheless, breadth-first can be superseded using an omniscient visit that chooses, at every step, the node of highest PageRank in the frontier. This paper discusses a related, and previously overlooked, measure of effectivity for crawl strategies: whether the graph obtained after a partial visit is in some sense representative of the underlying web graph as far as the computation of PageRank is concerned. More precisely, we are interested in determining how rapidly the computation of PageRank over the visited subgraph yields relative ranks that agre...