In an article in 1985, the computer scientist Andrew Yao, who could have won the AM TURING Award, claimed that among the hash tables with a specific set of properties, the best way to find a separate element or an empty point is to pass only through potential points – an approach known as a uniform butterfly. He also stated that at the worst case, where you are in search of the last open point, you can never be better than xHuman beings for 40 years, most computer scientists thought Yao’s guess was right.
Cropin did not retreat by conventional wisdom because of the simple reason it was unaware. “I did it without knowing Yao’s conjecture,” he said. His discoveries with small markers led to a new type of hash table – one of which did not rely on uniform exploration. And for this new hash table, the time required to display the worst and inserted data tailored (login x)2– faster than xHumanity was directly contrary to Yao’s conjecture. Farak-Calton and Kushazmool helped krapivin to show it (log x)2 Optimized and unique for the popular class of the hash tables that Yao wrote about is limited.
“This is a beautiful one that it solves and solves such a classic problem,” said Guy Beloch of Carnegie Melon.
“It’s not just that they rejected [Yao’s conjecture]They also found the best possible answer to his question. “” We could go for another 40 years before we know the right answer. “
In addition to rejecting Yao’s conjecture, the new article also contains what many find the astonishing result. This is related to a relevant situation, though slightly different: In 1985, Yao was not only displayed for the worst, but also on average all possible questions. He proved that the hash tables of special properties – including items that have “greedy”, this means that new elements must be at the first existing point – can never reach a moderate time better than logging in. xHuman
Frach-Calton, Cropin and Kozmool wanted to see if the same is applied to non-green hash tables. They showed that this did not do a non -green hash table with a medium query time that is much better than logging in xHuman beings. In fact, it does not depend on it x “You get a number,” something that is just a fixed and does not depend on how complete the hash table is, “said Farakh-Calton. “The fact that you can reach a constant average query time, regardless of the complete hash table, completely unexpected – even for the authors themselves.
The results of the team may not lead to urgent uses, but that’s not important, Kanoi said. “Better understanding of these types of data structures is important. You don’t know when the result is like this makes something that lets you do better in practice.”
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