In a Paper from 1985the computer scientist Andrew YaoWho would win the Amuring Prize, said that among the hash tables with a specific set of properties, the best way to find an individual or an empty place is to simply pass potential random places – an approach known as the uniform survey. He also said that, in the worst case, where you are looking for the last open open point, you can never do better than X. For 40 years, most computer scientists assumed that the conjecture of Yao was true.
Krapivin was not retained by conventional wisdom for the simple reason that he was not aware of it. “I did it without knowing Yao’s conjecture,” he said. His explorations with tiny pointers have led to a new type of hash table – which was not based on uniform surveys. And for this new chopping table, the time required for requests and insertions the worst cases is proportional to (newspaper X))2—Far faster than X. This result directly contradicts the Yao conjecture. Farach-Colton and Kuszmaul helped Krapivin show that (log X))2 is the optimal and unbeatable link for the popular class of hash tables that Yao had written.
“This result is beautiful in that it deals and solves such a classic problem,” said Guy Belloch from Carnegie Mellon.
“It is not only that they refuted (the conjecture of Yao), they also found the best possible answer to his question,” said Sepehr Assadi of the University of Waterloo. “We could have spent another 40 years before knowing the right answer.”
In addition to refuting the Yao conjecture, the new document also contains what many consider an even more surprising result. It concerns a related situation, although slightly different: in 1985, Yao examined not only the worst moments for requests, but also at the average time taken in all possible requests. It has proven that the hash tables with certain properties – especially those labeled “gourmet”, which means that new elements must be placed in the first available place – could never reach an average time better than the newspaper X.
Farach-Colton, Krapivin and Kuszmaul wanted to see if this same limit also applied to the non-sordid hash tables. They have shown that this is not the case by providing a counterexample, an unacit-cured owner with an average request time which is much, much better than the newspaper X. In fact, it does not depend on X at all. “You get a number,” said Farach-Colton, “something that is just a constant and does not depend on the full hash table.” The fact that you can get a constant medium request time, regardless of the fullness of the chopping table, was completely unexpected – even to the authors themselves.
Team results may not lead to any immediate application, but that’s not all that matters, said Conway. “It is important to better understand these types of data structures. You do not know when a result like this will unlock something that allows you to do better in practice. “”
Original story reprinted with the permission of Quanta Magazinean independent editorial publication of Simons Foundation whose mission is to improve the understanding of the public of science by covering the developments of research and the trends of mathematics and physical sciences and life.