Student UpenDS 40 years of Science of Data Science

In a 1985 paperComputer scientist Andrew YaoWho will continue to win the AM TURING Award, claims that among the hash tables with a specific set of real estate, the best way to find an individual element or empty space is to simply go through potential spots on a random basis – an approach known as even drilling. He also stated that in the worst scenario where you are looking for the last remaining place, you can never do better than xS For 40 years, most computer scientists have suggested that Yao’s assumption was true.

Krapivin was not detained by conventional wisdom for the simple reason that he did not know about it. “I did this without knowing Yao’s assumption,” he said. His studies with small directories led to a new type of hash table – one that did not rely on even drilling. And for this new hash table, the time required for the worst requests and insertions is proportional to (log x))²-The faster than xS This result directly contradicts Yao’s assumption. Farach-Colton and Kuszmaul helped Krapivin show that (Log x))² is the optimal, invincible bound for the popular class of hash tables he wrote about.

“This result is beautiful in that it is engaged in and solving such a classic problem,” said Guy Bleam Carnegie Melon.

“It’s not only that they denied (Yao’s assumption), they also found the best possible answer to his question,” said Sepper asad at the University of Waterloo. “We could have traveled another 40 years before we knew the right answer.”

Krapivin on the King’s College Bridge at the University of Cambridge. His new hash table can find and store data faster than researchers have ever considered possible.

Philip: Philip Amon for Quanta Magazine

In addition to the denial of YAO’s assumption, the new book also contains what many consider to be an even more insane result. It refers to a connected, albeit slightly different situation: in 1985, Yao looked not only in the worst time of requests, but also in the middle time, took away in all possible requests. He proved that hash tables of certain properties – including those that are marked with “greedy”, which means that the new elements must be placed in the first place – they can never reach an average time better than the diary xS

Farach-Kolton, Krapivin and Kusmaul wanted to see if the same border was applied to unequal hash tables. They showed that this did not happen by providing a counter-example, a parcel-on a medium-time time hash table that is much, much better than the diary xS In fact, it does not depend on x In general. “You get a number,” said Farach-Kolton, “something that is just a constant and does not depend on how full the hash table is.” The fact that you can achieve a constant average time for requests, regardless of the fullness of Hash Table, was completely unexpected – even for the authors themselves.

The results of the team may not lead to immediate applications, but this is not all that matters, Konway said. “It is important to better understand these types of data structures. You do not know when the result like this will unlock something that allows you to do better in practice. “

Original story reprinted with permission from How many magazineeditorial independent publication of Simons Foundation whose mission is to improve the social understanding of science by covering the development of research and trends in mathematics and physical and life sciences.