exist 1985 papercomputer scientist Andrew Yaowho will continue to win the AM Turing Award, he asserted that in a hash table with specific attributes, the best way to find a single element or empty space is to randomly browse potential attractions, a method called unified detection. He also said that in the worst case you are looking for the last remaining space you will never do better x. For 40 years, most computer scientists have believed that Yao’s conjecture is correct.
Krapingjin was not stopped by traditional wisdom for the simple reason because he was not aware of it. “I did this without knowing Yao’s conjecture,” he said. His exploration with tiny pointers led to a new type of hash table that did not rely on unified detection. For this new hash table, the time required for worst-case query and insertion is proportional to (log) x)2– Speed ratio x. This result is directly inconsistent with Yao Ming’s conjecture. Farach-Colton and Kuszmaul helped Krapivin show (log x)2 It is the best, unparalleled boundary of popular hash tables written by Yao.
“This result is beautiful because it solves and solves such a classic problem.” Guy Blelloch Carnegie Mellon.
“It’s not just them who refute it [Yao’s conjecture]they also found the best answer to his questions. ” Sepehr Assadi University of Waterloo. “We could have gone for another 40 years before we knew the right answer.”
In addition to refuting Yao Ming’s conjecture, the new paper also contains results that many people think are more surprising. This is related to the relevant situation, but is slightly different: in 1985, Yao not only looked at the worst query time, but also considered the average time of all possible query times. He proves that hash tables with certain properties (including lists marked “greedy”, which means that new elements must be placed in the first available location – thus the average time does not exceed the average time of the log. x.
Farach-Colton, Krapivin and Kuszmaul wanted to see if it works well for non-tobacco card tables as well. They show that it is not by providing a counterexample, a non-tobacco hash table whose average query time is much better than the log x. In fact, it doesn’t depend on x fundamental. “You get a number, which is just a constant, not depending on how full the hash table is.” You can reach a constant average query time, which is completely unexpected regardless of the fullness of the hash table, even the author itself.
Conway said the team’s results may not lead to any immediate application, but that doesn’t matter. “It is important to have a better understanding of this type of data structure. You don’t know when such an outcome will unlock things that will make you do better in practice.”
ability Reprinted with permission Quanta Magazineedit independent publications Simmons Foundation Its mission is to enhance public understanding of science by covering research developments and trends in mathematics and physics and life sciences.
