IN 1985 PaperIT specialist Andrew Yaowho would win the depreciation prize said that among the abbreviations tables with a specific set of properties, the best way to find an individual element or empty place is simply to go through potential random spots – the approach known as uniform probation. He also stated that in the worst scenario in which you are looking for the last remaining open place, you can never do better than X. For 40 years, most IT specialists assumed that Yao’s default was true.
Krapivin was not stopped by conventional wisdom for the straightforward reason that he was not aware of it. “I did it, not knowing about the supposition of Yao,” he said. His explorations with compact guidelines led to a up-to-date type of shortcut – one that did not consist of uniform probation. And for this up-to-date abbreviation table, the time required for the worst queries and insertion is proportional to (log X)2—Far faster than X. This result denied the assumption of Yao. Fearach-Colton and Kuszmaul helped Krapivin show this (log log X)2 It is the optimal, insurmountable, the popular class of Hash tables, which Yao wrote about.
“This result is beautiful because it solves and solves such a classic problem,” he said Guy Blellch Carnegie Mellon.
“They not only refuted [Yao’s conjecture]They also found the best possible answer to his question – he said Sepehr Assad Waterloo University. “We could have passed another 40 years before we got to know the right answer.”
In addition to overthrowing YAO, the up-to-date article also contains what many consider to be an even more amazing result. This applies to a related, though slightly different situation: in 1985 Yao looked not only the worst sometimes on queries, but also in the average time needed for all possible queries. He proved that the abbreviations tables with specific properties – including those that are marked as “greedy”, which means that up-to-date elements must be placed in the first place available – they can never achieve average time better than the log X.
Fearach-Colton, Krapivin and Kuszul wanted to see if the same limit also applies to unlimited hash tables. They showed that it wasn’t like that, giving a counter -lecture, an unlimited table of abbreviations with an average question time, much better X. In fact, it doesn’t X at all. “You get a number,” said Freech-Colton, “something that is simply constant and does not depend on how full the shortcut table is.” The fact that you can achieve a eternal average query time, regardless of the full table of shortcuts, was completely unexpected – even for the authors themselves.
Conway said that the team’s results may not lead to any immediate conclusions, but that’s not all that counts. “It is important to better understand this type of data structure. You don’t know when such a result will unlock something that will allow you to do better in practice. “
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