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Exploring a ‘Deep Web’ That Google Can’t Grasp Jeffrey D. Allred for The New York Times At the University of Utah, Prof. Juliana Freire is working on DeepPeep, an ambitious effort to index every public database online.   By ALEX WRIGHT One day last summer, Google’s search engine trundled quietly past a milestone. It added the one trillionth address to the list of Web pages it knows about. But as impossibly big as that number may seem, it represents only a fraction of the entire Web. Beyond those trillion pages lies an even vaster Web of hidden data: financial information, shopping catalogs, flight schedules, medical research and all kinds of other material stored in databases that remain largely invisible to search engines. The challenges that the major search engines face in penetrating this so-called Deep Web go a long way toward explaining why they still can’t provide satisfying answers to questions like “What’s the best fare from New York to London next Thursday?” The answers are readily available — if only the search engines knew how to find them. Now a new breed of technologies is taking shape that will extend the reach of search engines into the Web’s hidden corners. When that happens, it will do more than just improve the quality of search results — it may ultimately reshape the way many companies do business online. Search engines rely on programs known as crawlers (or spiders) that gather information by following the trails of hyperlinks that tie the Web together. While that approach works well for the pages that make up the surface Web, these programs have a harder time penetrating databases that are set up to respond to typed queries. “The crawlable Web is the tip of the iceberg,” says Anand Rajaraman,…