Together, Krapivin (now a graduate student at Cambridge University), Farach-Colton (now at New York University) and Kuszmaul have demonstrated in a January 2025 paper That this new hash table can indeed find elements faster than what was considered as possible. LN, they had refuted a conjecture for a long time to be true.
“This is an important article,” said Alex Conway From Cornell Tech to New York. “The hash tables are among the oldest data structures we have. And they are always one of the most effective ways to store data. However, open questions remain on how they work, he said. “This document responds a few in a surprising way.”
The hash tables have become ubiquitous in computer science, partly because of their simplicity and their ease of use. They are designed to allow users to do exactly three things: “request” (search) one element, delete an element or insert one in an empty slit. The first chopping tables date back to the early 1950s, and computer scientists have studied them and used them since. Among other things, researchers wanted to understand the speed limits of some of these operations. How much, for example, could a new research or insertion be possible?
The answer usually depends on the time it takes to find an empty place in a hash table. This, in turn, generally depends on the full hash table. Fullness can be described in terms of global percentage – this table is 50% full, that 90% – but researchers often treat much more complete tables. So, instead, they can use a whole number, indicated by XTo specify how 100%is the hash table. If X is 100, so the table is 99%full. If X is 1,000, the table is full at 99.9%. This fullness measure offers a practical means of assessing the time it takes to carry out actions such as questions or insertions.
Researchers have long since known that for certain common hash tables, the scheduled time required to make the worst possible insertion – to put an element, for example, the last open stain remaining – is proportional to X. “If your hatching table is 99%complete,” said Kuszmaul, “it is logical that you had to look at around 100 different positions to find a free slit.”
In a Paper from 1985the computer scientist Andrew YaoWho was going to win the AM Turing 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 under the Name of 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 a uniform survey. And for this new chopping table, the time required for requests and insertions the worst cases is proportional to (newspaper X))2 – much 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.”